Abstract

We introduce a general full-field propagation equation for optical waveguides, including both fundamental and higher order modes, and apply it to the investigation of spatial nonlinear effects of ultrafast and extremely broadband nonlinear processes in hollow-core optical fibers. The model is used to describe pulse propagation in gas-filled hollow-core waveguides including the full dispersion, Kerr, and ionization effects. We study third-harmonic generation into higher order modes, soliton emission of resonant dispersive waves into higher order modes, intermodal four-wave mixing, and Kerr-driven transverse self-focusing and plasma-defocusing, all in a gas-filled kagomé photonic crystal fiber system. In the latter case a form of waveguide-based filamentation is numerically predicted.

© 2014 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. R. H. Stolen, “Raman oscillation in glass optical waveguide,” Appl. Phys. Lett. 20, 62–64 (1972).
    [CrossRef]
  2. E. P. Ippen, “Stimulated Brillouin scattering in optical fibers,” Appl. Phys. Lett. 21, 539–541 (1972).
    [CrossRef]
  3. T. A. Birks, J. C. Knight, and P. St.J. Russell, “Endlessly single-mode photonic crystal fiber,” Opt. Lett. 22, 961–963 (1997).
    [CrossRef]
  4. K. J. Blow and D. Wood, “Theoretical description of transient stimulated Raman scattering in optical fibers,” IEEE J. Quantum Electron. 25, 2665–2673 (1989).
    [CrossRef]
  5. P. V. Mamyshev and S. V. Chernikov, “Ultrashort-pulse propagation in optical fibers,” Opt. Lett. 15, 1076–1078 (1990).
    [CrossRef]
  6. J. M. Dudley, G. Genty, and S. Coen, “Supercontinuum generation in photonic crystal fiber,” Rev. Mod. Phys. 78, 1135–1184 (2006).
    [CrossRef]
  7. A. V. Husakou and J. Herrmann, “Supercontinuum generation of higher-order solitons by fission in photonic crystal fibers,” Phys. Rev. Lett. 87, 203901 (2001).
    [CrossRef]
  8. M. Kolesik, J. V. Moloney, and M. Mlejnek, “Unidirectional optical pulse propagation equation,” Phys. Rev. Lett. 89, 283902 (2002).
    [CrossRef]
  9. M. Kolesik and J. Moloney, “Nonlinear optical pulse propagation simulation: from Maxwell’s to unidirectional equations,” Phys. Rev. E 70, 036604 (2004).
    [CrossRef]
  10. P. Kinsler, “Optical pulse propagation with minimal approximations,” Phys. Rev. A 81, 013819 (2010).
    [CrossRef]
  11. W. Chang, A. Nazarkin, J. C. Travers, J. Nold, P. Hölzer, N. Y. Joly, and P. St.J. Russell, “Influence of ionization on ultrafast gas-based nonlinear fiber optics,” Opt. Express 19, 21018 (2011).
    [CrossRef]
  12. F. Tani, J. C. Travers, and P. St.J. Russell, “PHz-wide supercontinua of nondispersing subcycle pulses generated by extreme modulational instability,” Phys. Rev. Lett. 111, 033902 (2013).
    [CrossRef]
  13. W. H. Renninger and F. W. Wise, “Optical solitons in graded-index multimode fibres,” Nat. Commun. 4, 1719 (2013).
    [CrossRef]
  14. Y. Chen, W. J. Wadsworth, and T. A. Birks, “Ultraviolet four-wave mixing in the LP02 fibre mode,” Opt. Lett. 38, 3747–3750 (2013).
  15. N. Bozinovic, Y. Yue, Y. Ren, M. Tur, P. Kristensen, H. Huang, A. E. Willner, and S. Ramachandran, “Terabit-scale orbital angular momentum mode division multiplexing in fibers,” Science 340, 1545–1548 (2013).
    [CrossRef]
  16. R. Ryf, S. Randel, A. H. Gnauck, C. Bolle, A. Sierra, S. Mumtaz, M. Esmaeelpour, E. C. Burrows, R.-J. Essiambre, P. J. Winzer, D. W. Peckham, A. H. McCurdy, and R. Lingle, “Mode-division multiplexing over 96  km of few-mode fiber using coherent 6×6 MIMO Processing,” J. Lightwave Technol. 30, 521–531 (2012).
    [CrossRef]
  17. J. C. Travers, W. Chang, J. Nold, N. Y. Joly, and P. St.J. Russell, “Ultrafast nonlinear optics in gas-filled hollow-core photonic crystal fibers,” J. Opt. Soc. Am. B 28, A11–A26 (2011).
    [CrossRef]
  18. K. F. Mak, J. C. Travers, N. Y. Joly, A. Abdolvand, and P. St.J. Russell, “Two techniques for temporal pulse compression in gas-filled hollow-core kagomé photonic crystal fiber,” Opt. Lett. 38, 3592–3595 (2013).
    [CrossRef]
  19. N. Y. Joly, J. Nold, W. Chang, P. Hölzer, A. Nazarkin, G. K. L. Wong, F. Biancalana, and P. St.J. Russell, “Bright spatially coherent wavelength-tunable deep-uv laser source using an ar-filled photonic crystal fiber,” Phys. Rev. Lett. 106, 203901 (2011).
    [CrossRef]
  20. K. F. Mak, J. C. Travers, P. Hölzer, N. Y. Joly, and P. St.J. Russell, “Tunable vacuum-UV to visible ultrafast pulse source based on gas-filled Kagome-PCF,” Opt. Express 21, 10942 (2013).
    [CrossRef]
  21. P. Hölzer, W. Chang, J. C. Travers, A. Nazarkin, J. Nold, N. Y. Joly, M. F. Saleh, F. Biancalana, and P. St.J. Russell, “Femtosecond nonlinear fiber optics in the ionization regime,” Phys. Rev. Lett. 107, 203901 (2011).
    [CrossRef]
  22. M. F. Saleh, W. Chang, P. Hölzer, A. Nazarkin, J. C. Travers, N. Y. Joly, P. St.J. Russell, and F. Biancalana, “Theory of photoionization-induced blueshift of ultrashort solitons in gas-filled hollow-core photonic crystal fibers,” Phys. Rev. Lett. 107, 203902 (2011).
    [CrossRef]
  23. W. Chang, P. Hölzer, J. C. Travers, and P. St.J. Russell, “Combined soliton pulse compression and plasma-related frequency upconversion in gas-filled photonic crystal fiber,” Opt. Lett. 38, 2984–2987 (2013).
    [CrossRef]
  24. J. Nold, P. Hölzer, N. Y. Joly, G. K. L. Wong, A. Nazarkin, A. Podlipensky, M. Scharrer, and P. St.J. Russell, “Pressure-controlled phase matching to third harmonic in Ar-filled hollow-core photonic crystal fiber,” Opt. Lett. 35, 2922–2924 (2010).
    [CrossRef]
  25. A. Hasegawa, “Self-confinement of multimode optical pulse in a glass fiber,” Opt. Lett. 5, 416–417 (1980).
    [CrossRef]
  26. B. Crosignani and P. D. Porto, “Soliton propagation in multimode optical fibers,” Opt. Lett. 6, 329–330 (1981).
    [CrossRef]
  27. C. R. Menyuk, “Stability of solitons in birefringent optical fibers. I: equal propagation amplitudes,” Opt. Lett. 12, 614–616 (1987).
    [CrossRef]
  28. F. Poletti and P. Horak, “Description of ultrashort pulse propagation in multimode optical fibers,” J. Opt. Soc. Am. B 25, 1645–1654 (2008).
    [CrossRef]
  29. C. L. Arnold, B. Zhou, S. Akturk, S. Chen, A. Couairon, and A. Mysyrowicz, “Pulse compression with planar hollow waveguides: a pathway towards relativistic intensity with table-top lasers,” New J. Phys. 12, 073015 (2010).
    [CrossRef]
  30. T. Popmintchev, M.-C. Chen, D. Popmintchev, P. Arpin, S. Brown, S. Alisauskas, G. Andriukaitis, T. Balciunas, O. D. Mucke, A. Pugzlys, A. Baltuska, B. Shim, S. E. Schrauth, A. Gaeta, C. Hernandez-Garcia, L. Plaja, A. Becker, A. Jaron-Becker, M. M. Murnane, and H. C. Kapteyn, “Bright coherent ultrahigh harmonics in the keV x-ray regime from mid-infrared femtosecond lasers,” Science 336, 1287–1291 (2012).
    [CrossRef]
  31. A. Couairon, E. Brambilla, T. Corti, D. Majus, O. Ramírez-Góngora, and M. Kolesik, “Practitioner’s guide to laser pulse propagation models and simulation,” Eur. Phys. J. Spec. Top. 199, 5–76 (2011).
    [CrossRef]
  32. I. Babushkin, S. Skupin, and J. Herrmann, “Generation of terahertz radiation from ionizing two-color laser pulses in Ar filled metallic hollow waveguides,” Opt. Express 18, 9658–9663 (2010).
    [CrossRef]
  33. A. W. Snyder and J. Love, Optical Waveguide Theory (Springer, 1983).
  34. M. Kolesik, P. Jakobsen, and J. V. Moloney, “Quantifying the limits of unidirectional ultrashort optical pulse propagation,” Phys. Rev. A 86, 035801 (2012).
    [CrossRef]
  35. M. Azhar, N. Y. Joly, J. C. Travers, and P. St.J. Russell, “Nonlinear optics in Xe-filled hollow-core PCF in high pressure and supercritical regimes,” Appl. Phys. B 112, 457–460 (2013).
  36. P. N. Butcher and D. Cotter, The Elements of Nonlinear Optics (Cambridge University, 1991).
  37. C. Köhler, L. Bergé, and S. Skupin, “Effect of nonlinear dispersion on pulse self-compression in a defocusing noble gas,” Physica D 240, 963–970 (2011).
    [CrossRef]
  38. D. P. Shelton, “Nonlinear-optical susceptibilities of gases measured at 1064 and 1319  nm,” Phys. Rev. A 42, 2578–2592 (1990).
    [CrossRef]
  39. H. J. Lehmeier, W. Leupacher, and A. Penzkofer, “Nonresonant third order hyperpolarizability of rare gases and N2 determined by third harmonic generation,” Opt. Commun. 56, 67–72 (1985).
    [CrossRef]
  40. V. P. Kalosha and J. Herrmann, “Phase relations, quasicontinuous spectra and subfemtosecond pulses in high-order stimulated Raman scattering with short-pulse excitation,” Phys. Rev. Lett. 85, 1226–1229 (2000).
    [CrossRef]
  41. J. Laegsgaard, “Mode profile dispersion in the generalised nonlinear Schr¨dinger equation,” Opt. Express 15, 16110–16123 (2007).
    [CrossRef]
  42. F. Poletti and P. Horak, “Dynamics of femtosecond supercontinuum generation in multimode fibers,” Opt. Express 17, 6134–6147 (2009).
    [CrossRef]
  43. S. C. Rae and K. Burnett, “Detailed simulations of plasma-induced spectral blueshifting,” Phys. Rev. A 46, 1084–1090 (1992).
    [CrossRef]
  44. G. Yudin and M. Ivanov, “Nonadiabatic tunnel ionization: looking inside a laser cycle,” Phys. Rev. A 64, 013409 (2001).
  45. V. S. Popov, “Tunnel and multiphoton ionization of atoms and ions in a strong laser field (Keldysh theory),” Physics-Uspekhi 47, 855–885 (2004).
    [CrossRef]
  46. M. Geissler, G. Tempea, A. Scrinzi, M. Schnürer, F. Krausz, and T. Brabec, “Light propagation in field-ionizing media: extreme nonlinear optics,” Phys. Rev. Lett. 83, 2930–2933 (1999).
    [CrossRef]
  47. J. Hult, “A fourth-order Runge-Kutta in the interaction picture method for simulating supercontinuum generation in optical fibers,” J. Lightwave Technol. 25, 3770–3775 (2007).
    [CrossRef]
  48. E. Hairer, S. P. Nørsett, and G. Wanner, Solving Ordinary Differential Equations I: Nonstiff Problems (Springer, 2010).
  49. S.-J. Im, A. Husakou, and J. Herrmann, “Guiding properties and dispersion control of kagome lattice hollow-core photonic crystal fibers,” Opt. Express 17, 13050–13058 (2009).
    [CrossRef]
  50. F. Benabid, J. C. Knight, G. Antonopoulos, and P. St.J. Russell, “Stimulated Raman scattering in hydrogen-filled hollow-core photonic crystal fiber,” Science 298, 399–402 (2002).
    [CrossRef]
  51. E. A. J. Marcatili and R. A. Schmeltzer, “Hollow metallic and dielectric waveguides for long distance optical transmission and lasers (long distance optical transmission in hollow dielectric and metal circular waveguides, examining normal mode propagation),” Bell Syst. Tech. J. 43, 1783–1809 (1964).
    [CrossRef]
  52. A. Börzsönyi, Z. Heiner, M. P. Kalashnikov, A. P. Kovács, and K. Osvay, “Dispersion measurement of inert gases and gas mixtures at 800  nm,” Appl. Opt. 47, 4856–4863 (2008).
    [CrossRef]
  53. P. K. A. Wai, H. H. Chen, and Y. C. Lee, “Radiations by ‘solitons’ at the zero group-dispersion wavelength of single-mode optical fibers,” Phys. Rev. A 41, 426–439 (1990).
    [CrossRef]
  54. N. Akhmediev and M. Karlsson, “Cherenkov radiation emitted by solitons in optical fibers,” Phys. Rev. A 51, 2602–2607 (1995).
    [CrossRef]
  55. A. V. Yulin, D. V. Skryabin, and P. St.J. Russell, “Four-wave mixing of linear waves and solitons in fibers with higher-orderdispersion,” Opt. Lett. 29, 2411–2413 (2004).
    [CrossRef]
  56. G. Tempea and T. Brabec, “Theory of self-focusing in a hollow waveguide,” Opt. Lett. 23, 762–764 (1998).
    [CrossRef]
  57. R. T. Chapman, T. J. Butcher, P. Horak, F. Poletti, J. G. Frey, and W. S. Brocklesby, “Modal effects on pump-pulse propagation in an Ar-filled capillary,” Opt. Express 18, 13279–13284 (2010).
    [CrossRef]
  58. G. Fibich and A. L. Gaeta, “Critical power for self-focusing in bulk media and in hollow waveguides,” Opt. Lett. 25, 335–337 (2000).
    [CrossRef]

2013

F. Tani, J. C. Travers, and P. St.J. Russell, “PHz-wide supercontinua of nondispersing subcycle pulses generated by extreme modulational instability,” Phys. Rev. Lett. 111, 033902 (2013).
[CrossRef]

W. H. Renninger and F. W. Wise, “Optical solitons in graded-index multimode fibres,” Nat. Commun. 4, 1719 (2013).
[CrossRef]

Y. Chen, W. J. Wadsworth, and T. A. Birks, “Ultraviolet four-wave mixing in the LP02 fibre mode,” Opt. Lett. 38, 3747–3750 (2013).

N. Bozinovic, Y. Yue, Y. Ren, M. Tur, P. Kristensen, H. Huang, A. E. Willner, and S. Ramachandran, “Terabit-scale orbital angular momentum mode division multiplexing in fibers,” Science 340, 1545–1548 (2013).
[CrossRef]

K. F. Mak, J. C. Travers, N. Y. Joly, A. Abdolvand, and P. St.J. Russell, “Two techniques for temporal pulse compression in gas-filled hollow-core kagomé photonic crystal fiber,” Opt. Lett. 38, 3592–3595 (2013).
[CrossRef]

K. F. Mak, J. C. Travers, P. Hölzer, N. Y. Joly, and P. St.J. Russell, “Tunable vacuum-UV to visible ultrafast pulse source based on gas-filled Kagome-PCF,” Opt. Express 21, 10942 (2013).
[CrossRef]

W. Chang, P. Hölzer, J. C. Travers, and P. St.J. Russell, “Combined soliton pulse compression and plasma-related frequency upconversion in gas-filled photonic crystal fiber,” Opt. Lett. 38, 2984–2987 (2013).
[CrossRef]

M. Azhar, N. Y. Joly, J. C. Travers, and P. St.J. Russell, “Nonlinear optics in Xe-filled hollow-core PCF in high pressure and supercritical regimes,” Appl. Phys. B 112, 457–460 (2013).

2012

T. Popmintchev, M.-C. Chen, D. Popmintchev, P. Arpin, S. Brown, S. Alisauskas, G. Andriukaitis, T. Balciunas, O. D. Mucke, A. Pugzlys, A. Baltuska, B. Shim, S. E. Schrauth, A. Gaeta, C. Hernandez-Garcia, L. Plaja, A. Becker, A. Jaron-Becker, M. M. Murnane, and H. C. Kapteyn, “Bright coherent ultrahigh harmonics in the keV x-ray regime from mid-infrared femtosecond lasers,” Science 336, 1287–1291 (2012).
[CrossRef]

M. Kolesik, P. Jakobsen, and J. V. Moloney, “Quantifying the limits of unidirectional ultrashort optical pulse propagation,” Phys. Rev. A 86, 035801 (2012).
[CrossRef]

R. Ryf, S. Randel, A. H. Gnauck, C. Bolle, A. Sierra, S. Mumtaz, M. Esmaeelpour, E. C. Burrows, R.-J. Essiambre, P. J. Winzer, D. W. Peckham, A. H. McCurdy, and R. Lingle, “Mode-division multiplexing over 96  km of few-mode fiber using coherent 6×6 MIMO Processing,” J. Lightwave Technol. 30, 521–531 (2012).
[CrossRef]

2011

J. C. Travers, W. Chang, J. Nold, N. Y. Joly, and P. St.J. Russell, “Ultrafast nonlinear optics in gas-filled hollow-core photonic crystal fibers,” J. Opt. Soc. Am. B 28, A11–A26 (2011).
[CrossRef]

N. Y. Joly, J. Nold, W. Chang, P. Hölzer, A. Nazarkin, G. K. L. Wong, F. Biancalana, and P. St.J. Russell, “Bright spatially coherent wavelength-tunable deep-uv laser source using an ar-filled photonic crystal fiber,” Phys. Rev. Lett. 106, 203901 (2011).
[CrossRef]

A. Couairon, E. Brambilla, T. Corti, D. Majus, O. Ramírez-Góngora, and M. Kolesik, “Practitioner’s guide to laser pulse propagation models and simulation,” Eur. Phys. J. Spec. Top. 199, 5–76 (2011).
[CrossRef]

C. Köhler, L. Bergé, and S. Skupin, “Effect of nonlinear dispersion on pulse self-compression in a defocusing noble gas,” Physica D 240, 963–970 (2011).
[CrossRef]

P. Hölzer, W. Chang, J. C. Travers, A. Nazarkin, J. Nold, N. Y. Joly, M. F. Saleh, F. Biancalana, and P. St.J. Russell, “Femtosecond nonlinear fiber optics in the ionization regime,” Phys. Rev. Lett. 107, 203901 (2011).
[CrossRef]

M. F. Saleh, W. Chang, P. Hölzer, A. Nazarkin, J. C. Travers, N. Y. Joly, P. St.J. Russell, and F. Biancalana, “Theory of photoionization-induced blueshift of ultrashort solitons in gas-filled hollow-core photonic crystal fibers,” Phys. Rev. Lett. 107, 203902 (2011).
[CrossRef]

W. Chang, A. Nazarkin, J. C. Travers, J. Nold, P. Hölzer, N. Y. Joly, and P. St.J. Russell, “Influence of ionization on ultrafast gas-based nonlinear fiber optics,” Opt. Express 19, 21018 (2011).
[CrossRef]

2010

J. Nold, P. Hölzer, N. Y. Joly, G. K. L. Wong, A. Nazarkin, A. Podlipensky, M. Scharrer, and P. St.J. Russell, “Pressure-controlled phase matching to third harmonic in Ar-filled hollow-core photonic crystal fiber,” Opt. Lett. 35, 2922–2924 (2010).
[CrossRef]

I. Babushkin, S. Skupin, and J. Herrmann, “Generation of terahertz radiation from ionizing two-color laser pulses in Ar filled metallic hollow waveguides,” Opt. Express 18, 9658–9663 (2010).
[CrossRef]

C. L. Arnold, B. Zhou, S. Akturk, S. Chen, A. Couairon, and A. Mysyrowicz, “Pulse compression with planar hollow waveguides: a pathway towards relativistic intensity with table-top lasers,” New J. Phys. 12, 073015 (2010).
[CrossRef]

P. Kinsler, “Optical pulse propagation with minimal approximations,” Phys. Rev. A 81, 013819 (2010).
[CrossRef]

R. T. Chapman, T. J. Butcher, P. Horak, F. Poletti, J. G. Frey, and W. S. Brocklesby, “Modal effects on pump-pulse propagation in an Ar-filled capillary,” Opt. Express 18, 13279–13284 (2010).
[CrossRef]

2009

S.-J. Im, A. Husakou, and J. Herrmann, “Guiding properties and dispersion control of kagome lattice hollow-core photonic crystal fibers,” Opt. Express 17, 13050–13058 (2009).
[CrossRef]

F. Poletti and P. Horak, “Dynamics of femtosecond supercontinuum generation in multimode fibers,” Opt. Express 17, 6134–6147 (2009).
[CrossRef]

2008

A. Börzsönyi, Z. Heiner, M. P. Kalashnikov, A. P. Kovács, and K. Osvay, “Dispersion measurement of inert gases and gas mixtures at 800  nm,” Appl. Opt. 47, 4856–4863 (2008).
[CrossRef]

F. Poletti and P. Horak, “Description of ultrashort pulse propagation in multimode optical fibers,” J. Opt. Soc. Am. B 25, 1645–1654 (2008).
[CrossRef]

2007

J. Laegsgaard, “Mode profile dispersion in the generalised nonlinear Schr¨dinger equation,” Opt. Express 15, 16110–16123 (2007).
[CrossRef]

J. Hult, “A fourth-order Runge-Kutta in the interaction picture method for simulating supercontinuum generation in optical fibers,” J. Lightwave Technol. 25, 3770–3775 (2007).
[CrossRef]

2006

J. M. Dudley, G. Genty, and S. Coen, “Supercontinuum generation in photonic crystal fiber,” Rev. Mod. Phys. 78, 1135–1184 (2006).
[CrossRef]

2004

M. Kolesik and J. Moloney, “Nonlinear optical pulse propagation simulation: from Maxwell’s to unidirectional equations,” Phys. Rev. E 70, 036604 (2004).
[CrossRef]

V. S. Popov, “Tunnel and multiphoton ionization of atoms and ions in a strong laser field (Keldysh theory),” Physics-Uspekhi 47, 855–885 (2004).
[CrossRef]

A. V. Yulin, D. V. Skryabin, and P. St.J. Russell, “Four-wave mixing of linear waves and solitons in fibers with higher-orderdispersion,” Opt. Lett. 29, 2411–2413 (2004).
[CrossRef]

2002

F. Benabid, J. C. Knight, G. Antonopoulos, and P. St.J. Russell, “Stimulated Raman scattering in hydrogen-filled hollow-core photonic crystal fiber,” Science 298, 399–402 (2002).
[CrossRef]

M. Kolesik, J. V. Moloney, and M. Mlejnek, “Unidirectional optical pulse propagation equation,” Phys. Rev. Lett. 89, 283902 (2002).
[CrossRef]

2001

A. V. Husakou and J. Herrmann, “Supercontinuum generation of higher-order solitons by fission in photonic crystal fibers,” Phys. Rev. Lett. 87, 203901 (2001).
[CrossRef]

G. Yudin and M. Ivanov, “Nonadiabatic tunnel ionization: looking inside a laser cycle,” Phys. Rev. A 64, 013409 (2001).

2000

V. P. Kalosha and J. Herrmann, “Phase relations, quasicontinuous spectra and subfemtosecond pulses in high-order stimulated Raman scattering with short-pulse excitation,” Phys. Rev. Lett. 85, 1226–1229 (2000).
[CrossRef]

G. Fibich and A. L. Gaeta, “Critical power for self-focusing in bulk media and in hollow waveguides,” Opt. Lett. 25, 335–337 (2000).
[CrossRef]

1999

M. Geissler, G. Tempea, A. Scrinzi, M. Schnürer, F. Krausz, and T. Brabec, “Light propagation in field-ionizing media: extreme nonlinear optics,” Phys. Rev. Lett. 83, 2930–2933 (1999).
[CrossRef]

1998

G. Tempea and T. Brabec, “Theory of self-focusing in a hollow waveguide,” Opt. Lett. 23, 762–764 (1998).
[CrossRef]

1997

T. A. Birks, J. C. Knight, and P. St.J. Russell, “Endlessly single-mode photonic crystal fiber,” Opt. Lett. 22, 961–963 (1997).
[CrossRef]

1995

N. Akhmediev and M. Karlsson, “Cherenkov radiation emitted by solitons in optical fibers,” Phys. Rev. A 51, 2602–2607 (1995).
[CrossRef]

1992

S. C. Rae and K. Burnett, “Detailed simulations of plasma-induced spectral blueshifting,” Phys. Rev. A 46, 1084–1090 (1992).
[CrossRef]

1990

P. K. A. Wai, H. H. Chen, and Y. C. Lee, “Radiations by ‘solitons’ at the zero group-dispersion wavelength of single-mode optical fibers,” Phys. Rev. A 41, 426–439 (1990).
[CrossRef]

P. V. Mamyshev and S. V. Chernikov, “Ultrashort-pulse propagation in optical fibers,” Opt. Lett. 15, 1076–1078 (1990).
[CrossRef]

D. P. Shelton, “Nonlinear-optical susceptibilities of gases measured at 1064 and 1319  nm,” Phys. Rev. A 42, 2578–2592 (1990).
[CrossRef]

1989

K. J. Blow and D. Wood, “Theoretical description of transient stimulated Raman scattering in optical fibers,” IEEE J. Quantum Electron. 25, 2665–2673 (1989).
[CrossRef]

1987

C. R. Menyuk, “Stability of solitons in birefringent optical fibers. I: equal propagation amplitudes,” Opt. Lett. 12, 614–616 (1987).
[CrossRef]

1985

H. J. Lehmeier, W. Leupacher, and A. Penzkofer, “Nonresonant third order hyperpolarizability of rare gases and N2 determined by third harmonic generation,” Opt. Commun. 56, 67–72 (1985).
[CrossRef]

1981

B. Crosignani and P. D. Porto, “Soliton propagation in multimode optical fibers,” Opt. Lett. 6, 329–330 (1981).
[CrossRef]

1980

A. Hasegawa, “Self-confinement of multimode optical pulse in a glass fiber,” Opt. Lett. 5, 416–417 (1980).
[CrossRef]

1972

R. H. Stolen, “Raman oscillation in glass optical waveguide,” Appl. Phys. Lett. 20, 62–64 (1972).
[CrossRef]

E. P. Ippen, “Stimulated Brillouin scattering in optical fibers,” Appl. Phys. Lett. 21, 539–541 (1972).
[CrossRef]

1964

E. A. J. Marcatili and R. A. Schmeltzer, “Hollow metallic and dielectric waveguides for long distance optical transmission and lasers (long distance optical transmission in hollow dielectric and metal circular waveguides, examining normal mode propagation),” Bell Syst. Tech. J. 43, 1783–1809 (1964).
[CrossRef]

Abdolvand, A.

K. F. Mak, J. C. Travers, N. Y. Joly, A. Abdolvand, and P. St.J. Russell, “Two techniques for temporal pulse compression in gas-filled hollow-core kagomé photonic crystal fiber,” Opt. Lett. 38, 3592–3595 (2013).
[CrossRef]

Akhmediev, N.

N. Akhmediev and M. Karlsson, “Cherenkov radiation emitted by solitons in optical fibers,” Phys. Rev. A 51, 2602–2607 (1995).
[CrossRef]

Akturk, S.

C. L. Arnold, B. Zhou, S. Akturk, S. Chen, A. Couairon, and A. Mysyrowicz, “Pulse compression with planar hollow waveguides: a pathway towards relativistic intensity with table-top lasers,” New J. Phys. 12, 073015 (2010).
[CrossRef]

Alisauskas, S.

T. Popmintchev, M.-C. Chen, D. Popmintchev, P. Arpin, S. Brown, S. Alisauskas, G. Andriukaitis, T. Balciunas, O. D. Mucke, A. Pugzlys, A. Baltuska, B. Shim, S. E. Schrauth, A. Gaeta, C. Hernandez-Garcia, L. Plaja, A. Becker, A. Jaron-Becker, M. M. Murnane, and H. C. Kapteyn, “Bright coherent ultrahigh harmonics in the keV x-ray regime from mid-infrared femtosecond lasers,” Science 336, 1287–1291 (2012).
[CrossRef]

Andriukaitis, G.

T. Popmintchev, M.-C. Chen, D. Popmintchev, P. Arpin, S. Brown, S. Alisauskas, G. Andriukaitis, T. Balciunas, O. D. Mucke, A. Pugzlys, A. Baltuska, B. Shim, S. E. Schrauth, A. Gaeta, C. Hernandez-Garcia, L. Plaja, A. Becker, A. Jaron-Becker, M. M. Murnane, and H. C. Kapteyn, “Bright coherent ultrahigh harmonics in the keV x-ray regime from mid-infrared femtosecond lasers,” Science 336, 1287–1291 (2012).
[CrossRef]

Antonopoulos, G.

F. Benabid, J. C. Knight, G. Antonopoulos, and P. St.J. Russell, “Stimulated Raman scattering in hydrogen-filled hollow-core photonic crystal fiber,” Science 298, 399–402 (2002).
[CrossRef]

Arnold, C. L.

C. L. Arnold, B. Zhou, S. Akturk, S. Chen, A. Couairon, and A. Mysyrowicz, “Pulse compression with planar hollow waveguides: a pathway towards relativistic intensity with table-top lasers,” New J. Phys. 12, 073015 (2010).
[CrossRef]

Arpin, P.

T. Popmintchev, M.-C. Chen, D. Popmintchev, P. Arpin, S. Brown, S. Alisauskas, G. Andriukaitis, T. Balciunas, O. D. Mucke, A. Pugzlys, A. Baltuska, B. Shim, S. E. Schrauth, A. Gaeta, C. Hernandez-Garcia, L. Plaja, A. Becker, A. Jaron-Becker, M. M. Murnane, and H. C. Kapteyn, “Bright coherent ultrahigh harmonics in the keV x-ray regime from mid-infrared femtosecond lasers,” Science 336, 1287–1291 (2012).
[CrossRef]

Azhar, M.

M. Azhar, N. Y. Joly, J. C. Travers, and P. St.J. Russell, “Nonlinear optics in Xe-filled hollow-core PCF in high pressure and supercritical regimes,” Appl. Phys. B 112, 457–460 (2013).

Babushkin, I.

I. Babushkin, S. Skupin, and J. Herrmann, “Generation of terahertz radiation from ionizing two-color laser pulses in Ar filled metallic hollow waveguides,” Opt. Express 18, 9658–9663 (2010).
[CrossRef]

Balciunas, T.

T. Popmintchev, M.-C. Chen, D. Popmintchev, P. Arpin, S. Brown, S. Alisauskas, G. Andriukaitis, T. Balciunas, O. D. Mucke, A. Pugzlys, A. Baltuska, B. Shim, S. E. Schrauth, A. Gaeta, C. Hernandez-Garcia, L. Plaja, A. Becker, A. Jaron-Becker, M. M. Murnane, and H. C. Kapteyn, “Bright coherent ultrahigh harmonics in the keV x-ray regime from mid-infrared femtosecond lasers,” Science 336, 1287–1291 (2012).
[CrossRef]

Baltuska, A.

T. Popmintchev, M.-C. Chen, D. Popmintchev, P. Arpin, S. Brown, S. Alisauskas, G. Andriukaitis, T. Balciunas, O. D. Mucke, A. Pugzlys, A. Baltuska, B. Shim, S. E. Schrauth, A. Gaeta, C. Hernandez-Garcia, L. Plaja, A. Becker, A. Jaron-Becker, M. M. Murnane, and H. C. Kapteyn, “Bright coherent ultrahigh harmonics in the keV x-ray regime from mid-infrared femtosecond lasers,” Science 336, 1287–1291 (2012).
[CrossRef]

Becker, A.

T. Popmintchev, M.-C. Chen, D. Popmintchev, P. Arpin, S. Brown, S. Alisauskas, G. Andriukaitis, T. Balciunas, O. D. Mucke, A. Pugzlys, A. Baltuska, B. Shim, S. E. Schrauth, A. Gaeta, C. Hernandez-Garcia, L. Plaja, A. Becker, A. Jaron-Becker, M. M. Murnane, and H. C. Kapteyn, “Bright coherent ultrahigh harmonics in the keV x-ray regime from mid-infrared femtosecond lasers,” Science 336, 1287–1291 (2012).
[CrossRef]

Benabid, F.

F. Benabid, J. C. Knight, G. Antonopoulos, and P. St.J. Russell, “Stimulated Raman scattering in hydrogen-filled hollow-core photonic crystal fiber,” Science 298, 399–402 (2002).
[CrossRef]

Bergé, L.

C. Köhler, L. Bergé, and S. Skupin, “Effect of nonlinear dispersion on pulse self-compression in a defocusing noble gas,” Physica D 240, 963–970 (2011).
[CrossRef]

Biancalana, F.

N. Y. Joly, J. Nold, W. Chang, P. Hölzer, A. Nazarkin, G. K. L. Wong, F. Biancalana, and P. St.J. Russell, “Bright spatially coherent wavelength-tunable deep-uv laser source using an ar-filled photonic crystal fiber,” Phys. Rev. Lett. 106, 203901 (2011).
[CrossRef]

P. Hölzer, W. Chang, J. C. Travers, A. Nazarkin, J. Nold, N. Y. Joly, M. F. Saleh, F. Biancalana, and P. St.J. Russell, “Femtosecond nonlinear fiber optics in the ionization regime,” Phys. Rev. Lett. 107, 203901 (2011).
[CrossRef]

M. F. Saleh, W. Chang, P. Hölzer, A. Nazarkin, J. C. Travers, N. Y. Joly, P. St.J. Russell, and F. Biancalana, “Theory of photoionization-induced blueshift of ultrashort solitons in gas-filled hollow-core photonic crystal fibers,” Phys. Rev. Lett. 107, 203902 (2011).
[CrossRef]

Birks, T. A.

Y. Chen, W. J. Wadsworth, and T. A. Birks, “Ultraviolet four-wave mixing in the LP02 fibre mode,” Opt. Lett. 38, 3747–3750 (2013).

T. A. Birks, J. C. Knight, and P. St.J. Russell, “Endlessly single-mode photonic crystal fiber,” Opt. Lett. 22, 961–963 (1997).
[CrossRef]

Blow, K. J.

K. J. Blow and D. Wood, “Theoretical description of transient stimulated Raman scattering in optical fibers,” IEEE J. Quantum Electron. 25, 2665–2673 (1989).
[CrossRef]

Bolle, C.

R. Ryf, S. Randel, A. H. Gnauck, C. Bolle, A. Sierra, S. Mumtaz, M. Esmaeelpour, E. C. Burrows, R.-J. Essiambre, P. J. Winzer, D. W. Peckham, A. H. McCurdy, and R. Lingle, “Mode-division multiplexing over 96  km of few-mode fiber using coherent 6×6 MIMO Processing,” J. Lightwave Technol. 30, 521–531 (2012).
[CrossRef]

Börzsönyi, A.

A. Börzsönyi, Z. Heiner, M. P. Kalashnikov, A. P. Kovács, and K. Osvay, “Dispersion measurement of inert gases and gas mixtures at 800  nm,” Appl. Opt. 47, 4856–4863 (2008).
[CrossRef]

Bozinovic, N.

N. Bozinovic, Y. Yue, Y. Ren, M. Tur, P. Kristensen, H. Huang, A. E. Willner, and S. Ramachandran, “Terabit-scale orbital angular momentum mode division multiplexing in fibers,” Science 340, 1545–1548 (2013).
[CrossRef]

Brabec, T.

M. Geissler, G. Tempea, A. Scrinzi, M. Schnürer, F. Krausz, and T. Brabec, “Light propagation in field-ionizing media: extreme nonlinear optics,” Phys. Rev. Lett. 83, 2930–2933 (1999).
[CrossRef]

G. Tempea and T. Brabec, “Theory of self-focusing in a hollow waveguide,” Opt. Lett. 23, 762–764 (1998).
[CrossRef]

Brambilla, E.

A. Couairon, E. Brambilla, T. Corti, D. Majus, O. Ramírez-Góngora, and M. Kolesik, “Practitioner’s guide to laser pulse propagation models and simulation,” Eur. Phys. J. Spec. Top. 199, 5–76 (2011).
[CrossRef]

Brocklesby, W. S.

R. T. Chapman, T. J. Butcher, P. Horak, F. Poletti, J. G. Frey, and W. S. Brocklesby, “Modal effects on pump-pulse propagation in an Ar-filled capillary,” Opt. Express 18, 13279–13284 (2010).
[CrossRef]

Brown, S.

T. Popmintchev, M.-C. Chen, D. Popmintchev, P. Arpin, S. Brown, S. Alisauskas, G. Andriukaitis, T. Balciunas, O. D. Mucke, A. Pugzlys, A. Baltuska, B. Shim, S. E. Schrauth, A. Gaeta, C. Hernandez-Garcia, L. Plaja, A. Becker, A. Jaron-Becker, M. M. Murnane, and H. C. Kapteyn, “Bright coherent ultrahigh harmonics in the keV x-ray regime from mid-infrared femtosecond lasers,” Science 336, 1287–1291 (2012).
[CrossRef]

Burnett, K.

S. C. Rae and K. Burnett, “Detailed simulations of plasma-induced spectral blueshifting,” Phys. Rev. A 46, 1084–1090 (1992).
[CrossRef]

Burrows, E. C.

R. Ryf, S. Randel, A. H. Gnauck, C. Bolle, A. Sierra, S. Mumtaz, M. Esmaeelpour, E. C. Burrows, R.-J. Essiambre, P. J. Winzer, D. W. Peckham, A. H. McCurdy, and R. Lingle, “Mode-division multiplexing over 96  km of few-mode fiber using coherent 6×6 MIMO Processing,” J. Lightwave Technol. 30, 521–531 (2012).
[CrossRef]

Butcher, P. N.

P. N. Butcher and D. Cotter, The Elements of Nonlinear Optics (Cambridge University, 1991).

Butcher, T. J.

R. T. Chapman, T. J. Butcher, P. Horak, F. Poletti, J. G. Frey, and W. S. Brocklesby, “Modal effects on pump-pulse propagation in an Ar-filled capillary,” Opt. Express 18, 13279–13284 (2010).
[CrossRef]

Chang, W.

W. Chang, P. Hölzer, J. C. Travers, and P. St.J. Russell, “Combined soliton pulse compression and plasma-related frequency upconversion in gas-filled photonic crystal fiber,” Opt. Lett. 38, 2984–2987 (2013).
[CrossRef]

M. F. Saleh, W. Chang, P. Hölzer, A. Nazarkin, J. C. Travers, N. Y. Joly, P. St.J. Russell, and F. Biancalana, “Theory of photoionization-induced blueshift of ultrashort solitons in gas-filled hollow-core photonic crystal fibers,” Phys. Rev. Lett. 107, 203902 (2011).
[CrossRef]

P. Hölzer, W. Chang, J. C. Travers, A. Nazarkin, J. Nold, N. Y. Joly, M. F. Saleh, F. Biancalana, and P. St.J. Russell, “Femtosecond nonlinear fiber optics in the ionization regime,” Phys. Rev. Lett. 107, 203901 (2011).
[CrossRef]

N. Y. Joly, J. Nold, W. Chang, P. Hölzer, A. Nazarkin, G. K. L. Wong, F. Biancalana, and P. St.J. Russell, “Bright spatially coherent wavelength-tunable deep-uv laser source using an ar-filled photonic crystal fiber,” Phys. Rev. Lett. 106, 203901 (2011).
[CrossRef]

J. C. Travers, W. Chang, J. Nold, N. Y. Joly, and P. St.J. Russell, “Ultrafast nonlinear optics in gas-filled hollow-core photonic crystal fibers,” J. Opt. Soc. Am. B 28, A11–A26 (2011).
[CrossRef]

W. Chang, A. Nazarkin, J. C. Travers, J. Nold, P. Hölzer, N. Y. Joly, and P. St.J. Russell, “Influence of ionization on ultrafast gas-based nonlinear fiber optics,” Opt. Express 19, 21018 (2011).
[CrossRef]

Chapman, R. T.

R. T. Chapman, T. J. Butcher, P. Horak, F. Poletti, J. G. Frey, and W. S. Brocklesby, “Modal effects on pump-pulse propagation in an Ar-filled capillary,” Opt. Express 18, 13279–13284 (2010).
[CrossRef]

Chen, H. H.

P. K. A. Wai, H. H. Chen, and Y. C. Lee, “Radiations by ‘solitons’ at the zero group-dispersion wavelength of single-mode optical fibers,” Phys. Rev. A 41, 426–439 (1990).
[CrossRef]

Chen, M.-C.

T. Popmintchev, M.-C. Chen, D. Popmintchev, P. Arpin, S. Brown, S. Alisauskas, G. Andriukaitis, T. Balciunas, O. D. Mucke, A. Pugzlys, A. Baltuska, B. Shim, S. E. Schrauth, A. Gaeta, C. Hernandez-Garcia, L. Plaja, A. Becker, A. Jaron-Becker, M. M. Murnane, and H. C. Kapteyn, “Bright coherent ultrahigh harmonics in the keV x-ray regime from mid-infrared femtosecond lasers,” Science 336, 1287–1291 (2012).
[CrossRef]

Chen, S.

C. L. Arnold, B. Zhou, S. Akturk, S. Chen, A. Couairon, and A. Mysyrowicz, “Pulse compression with planar hollow waveguides: a pathway towards relativistic intensity with table-top lasers,” New J. Phys. 12, 073015 (2010).
[CrossRef]

Chen, Y.

Y. Chen, W. J. Wadsworth, and T. A. Birks, “Ultraviolet four-wave mixing in the LP02 fibre mode,” Opt. Lett. 38, 3747–3750 (2013).

Chernikov, S. V.

P. V. Mamyshev and S. V. Chernikov, “Ultrashort-pulse propagation in optical fibers,” Opt. Lett. 15, 1076–1078 (1990).
[CrossRef]

Coen, S.

J. M. Dudley, G. Genty, and S. Coen, “Supercontinuum generation in photonic crystal fiber,” Rev. Mod. Phys. 78, 1135–1184 (2006).
[CrossRef]

Corti, T.

A. Couairon, E. Brambilla, T. Corti, D. Majus, O. Ramírez-Góngora, and M. Kolesik, “Practitioner’s guide to laser pulse propagation models and simulation,” Eur. Phys. J. Spec. Top. 199, 5–76 (2011).
[CrossRef]

Cotter, D.

P. N. Butcher and D. Cotter, The Elements of Nonlinear Optics (Cambridge University, 1991).

Couairon, A.

A. Couairon, E. Brambilla, T. Corti, D. Majus, O. Ramírez-Góngora, and M. Kolesik, “Practitioner’s guide to laser pulse propagation models and simulation,” Eur. Phys. J. Spec. Top. 199, 5–76 (2011).
[CrossRef]

C. L. Arnold, B. Zhou, S. Akturk, S. Chen, A. Couairon, and A. Mysyrowicz, “Pulse compression with planar hollow waveguides: a pathway towards relativistic intensity with table-top lasers,” New J. Phys. 12, 073015 (2010).
[CrossRef]

Crosignani, B.

B. Crosignani and P. D. Porto, “Soliton propagation in multimode optical fibers,” Opt. Lett. 6, 329–330 (1981).
[CrossRef]

Dudley, J. M.

J. M. Dudley, G. Genty, and S. Coen, “Supercontinuum generation in photonic crystal fiber,” Rev. Mod. Phys. 78, 1135–1184 (2006).
[CrossRef]

Esmaeelpour, M.

R. Ryf, S. Randel, A. H. Gnauck, C. Bolle, A. Sierra, S. Mumtaz, M. Esmaeelpour, E. C. Burrows, R.-J. Essiambre, P. J. Winzer, D. W. Peckham, A. H. McCurdy, and R. Lingle, “Mode-division multiplexing over 96  km of few-mode fiber using coherent 6×6 MIMO Processing,” J. Lightwave Technol. 30, 521–531 (2012).
[CrossRef]

Essiambre, R.-J.

R. Ryf, S. Randel, A. H. Gnauck, C. Bolle, A. Sierra, S. Mumtaz, M. Esmaeelpour, E. C. Burrows, R.-J. Essiambre, P. J. Winzer, D. W. Peckham, A. H. McCurdy, and R. Lingle, “Mode-division multiplexing over 96  km of few-mode fiber using coherent 6×6 MIMO Processing,” J. Lightwave Technol. 30, 521–531 (2012).
[CrossRef]

Fibich, G.

G. Fibich and A. L. Gaeta, “Critical power for self-focusing in bulk media and in hollow waveguides,” Opt. Lett. 25, 335–337 (2000).
[CrossRef]

Frey, J. G.

R. T. Chapman, T. J. Butcher, P. Horak, F. Poletti, J. G. Frey, and W. S. Brocklesby, “Modal effects on pump-pulse propagation in an Ar-filled capillary,” Opt. Express 18, 13279–13284 (2010).
[CrossRef]

Gaeta, A.

T. Popmintchev, M.-C. Chen, D. Popmintchev, P. Arpin, S. Brown, S. Alisauskas, G. Andriukaitis, T. Balciunas, O. D. Mucke, A. Pugzlys, A. Baltuska, B. Shim, S. E. Schrauth, A. Gaeta, C. Hernandez-Garcia, L. Plaja, A. Becker, A. Jaron-Becker, M. M. Murnane, and H. C. Kapteyn, “Bright coherent ultrahigh harmonics in the keV x-ray regime from mid-infrared femtosecond lasers,” Science 336, 1287–1291 (2012).
[CrossRef]

Gaeta, A. L.

G. Fibich and A. L. Gaeta, “Critical power for self-focusing in bulk media and in hollow waveguides,” Opt. Lett. 25, 335–337 (2000).
[CrossRef]

Geissler, M.

M. Geissler, G. Tempea, A. Scrinzi, M. Schnürer, F. Krausz, and T. Brabec, “Light propagation in field-ionizing media: extreme nonlinear optics,” Phys. Rev. Lett. 83, 2930–2933 (1999).
[CrossRef]

Genty, G.

J. M. Dudley, G. Genty, and S. Coen, “Supercontinuum generation in photonic crystal fiber,” Rev. Mod. Phys. 78, 1135–1184 (2006).
[CrossRef]

Gnauck, A. H.

R. Ryf, S. Randel, A. H. Gnauck, C. Bolle, A. Sierra, S. Mumtaz, M. Esmaeelpour, E. C. Burrows, R.-J. Essiambre, P. J. Winzer, D. W. Peckham, A. H. McCurdy, and R. Lingle, “Mode-division multiplexing over 96  km of few-mode fiber using coherent 6×6 MIMO Processing,” J. Lightwave Technol. 30, 521–531 (2012).
[CrossRef]

Hairer, E.

E. Hairer, S. P. Nørsett, and G. Wanner, Solving Ordinary Differential Equations I: Nonstiff Problems (Springer, 2010).

Hasegawa, A.

A. Hasegawa, “Self-confinement of multimode optical pulse in a glass fiber,” Opt. Lett. 5, 416–417 (1980).
[CrossRef]

Heiner, Z.

A. Börzsönyi, Z. Heiner, M. P. Kalashnikov, A. P. Kovács, and K. Osvay, “Dispersion measurement of inert gases and gas mixtures at 800  nm,” Appl. Opt. 47, 4856–4863 (2008).
[CrossRef]

Hernandez-Garcia, C.

T. Popmintchev, M.-C. Chen, D. Popmintchev, P. Arpin, S. Brown, S. Alisauskas, G. Andriukaitis, T. Balciunas, O. D. Mucke, A. Pugzlys, A. Baltuska, B. Shim, S. E. Schrauth, A. Gaeta, C. Hernandez-Garcia, L. Plaja, A. Becker, A. Jaron-Becker, M. M. Murnane, and H. C. Kapteyn, “Bright coherent ultrahigh harmonics in the keV x-ray regime from mid-infrared femtosecond lasers,” Science 336, 1287–1291 (2012).
[CrossRef]

Herrmann, J.

I. Babushkin, S. Skupin, and J. Herrmann, “Generation of terahertz radiation from ionizing two-color laser pulses in Ar filled metallic hollow waveguides,” Opt. Express 18, 9658–9663 (2010).
[CrossRef]

S.-J. Im, A. Husakou, and J. Herrmann, “Guiding properties and dispersion control of kagome lattice hollow-core photonic crystal fibers,” Opt. Express 17, 13050–13058 (2009).
[CrossRef]

A. V. Husakou and J. Herrmann, “Supercontinuum generation of higher-order solitons by fission in photonic crystal fibers,” Phys. Rev. Lett. 87, 203901 (2001).
[CrossRef]

V. P. Kalosha and J. Herrmann, “Phase relations, quasicontinuous spectra and subfemtosecond pulses in high-order stimulated Raman scattering with short-pulse excitation,” Phys. Rev. Lett. 85, 1226–1229 (2000).
[CrossRef]

Hölzer, P.

K. F. Mak, J. C. Travers, P. Hölzer, N. Y. Joly, and P. St.J. Russell, “Tunable vacuum-UV to visible ultrafast pulse source based on gas-filled Kagome-PCF,” Opt. Express 21, 10942 (2013).
[CrossRef]

W. Chang, P. Hölzer, J. C. Travers, and P. St.J. Russell, “Combined soliton pulse compression and plasma-related frequency upconversion in gas-filled photonic crystal fiber,” Opt. Lett. 38, 2984–2987 (2013).
[CrossRef]

M. F. Saleh, W. Chang, P. Hölzer, A. Nazarkin, J. C. Travers, N. Y. Joly, P. St.J. Russell, and F. Biancalana, “Theory of photoionization-induced blueshift of ultrashort solitons in gas-filled hollow-core photonic crystal fibers,” Phys. Rev. Lett. 107, 203902 (2011).
[CrossRef]

P. Hölzer, W. Chang, J. C. Travers, A. Nazarkin, J. Nold, N. Y. Joly, M. F. Saleh, F. Biancalana, and P. St.J. Russell, “Femtosecond nonlinear fiber optics in the ionization regime,” Phys. Rev. Lett. 107, 203901 (2011).
[CrossRef]

W. Chang, A. Nazarkin, J. C. Travers, J. Nold, P. Hölzer, N. Y. Joly, and P. St.J. Russell, “Influence of ionization on ultrafast gas-based nonlinear fiber optics,” Opt. Express 19, 21018 (2011).
[CrossRef]

N. Y. Joly, J. Nold, W. Chang, P. Hölzer, A. Nazarkin, G. K. L. Wong, F. Biancalana, and P. St.J. Russell, “Bright spatially coherent wavelength-tunable deep-uv laser source using an ar-filled photonic crystal fiber,” Phys. Rev. Lett. 106, 203901 (2011).
[CrossRef]

J. Nold, P. Hölzer, N. Y. Joly, G. K. L. Wong, A. Nazarkin, A. Podlipensky, M. Scharrer, and P. St.J. Russell, “Pressure-controlled phase matching to third harmonic in Ar-filled hollow-core photonic crystal fiber,” Opt. Lett. 35, 2922–2924 (2010).
[CrossRef]

Horak, P.

R. T. Chapman, T. J. Butcher, P. Horak, F. Poletti, J. G. Frey, and W. S. Brocklesby, “Modal effects on pump-pulse propagation in an Ar-filled capillary,” Opt. Express 18, 13279–13284 (2010).
[CrossRef]

F. Poletti and P. Horak, “Dynamics of femtosecond supercontinuum generation in multimode fibers,” Opt. Express 17, 6134–6147 (2009).
[CrossRef]

F. Poletti and P. Horak, “Description of ultrashort pulse propagation in multimode optical fibers,” J. Opt. Soc. Am. B 25, 1645–1654 (2008).
[CrossRef]

Huang, H.

N. Bozinovic, Y. Yue, Y. Ren, M. Tur, P. Kristensen, H. Huang, A. E. Willner, and S. Ramachandran, “Terabit-scale orbital angular momentum mode division multiplexing in fibers,” Science 340, 1545–1548 (2013).
[CrossRef]

Hult, J.

J. Hult, “A fourth-order Runge-Kutta in the interaction picture method for simulating supercontinuum generation in optical fibers,” J. Lightwave Technol. 25, 3770–3775 (2007).
[CrossRef]

Husakou, A.

S.-J. Im, A. Husakou, and J. Herrmann, “Guiding properties and dispersion control of kagome lattice hollow-core photonic crystal fibers,” Opt. Express 17, 13050–13058 (2009).
[CrossRef]

Husakou, A. V.

A. V. Husakou and J. Herrmann, “Supercontinuum generation of higher-order solitons by fission in photonic crystal fibers,” Phys. Rev. Lett. 87, 203901 (2001).
[CrossRef]

Im, S.-J.

S.-J. Im, A. Husakou, and J. Herrmann, “Guiding properties and dispersion control of kagome lattice hollow-core photonic crystal fibers,” Opt. Express 17, 13050–13058 (2009).
[CrossRef]

Ippen, E. P.

E. P. Ippen, “Stimulated Brillouin scattering in optical fibers,” Appl. Phys. Lett. 21, 539–541 (1972).
[CrossRef]

Ivanov, M.

G. Yudin and M. Ivanov, “Nonadiabatic tunnel ionization: looking inside a laser cycle,” Phys. Rev. A 64, 013409 (2001).

Jakobsen, P.

M. Kolesik, P. Jakobsen, and J. V. Moloney, “Quantifying the limits of unidirectional ultrashort optical pulse propagation,” Phys. Rev. A 86, 035801 (2012).
[CrossRef]

Jaron-Becker, A.

T. Popmintchev, M.-C. Chen, D. Popmintchev, P. Arpin, S. Brown, S. Alisauskas, G. Andriukaitis, T. Balciunas, O. D. Mucke, A. Pugzlys, A. Baltuska, B. Shim, S. E. Schrauth, A. Gaeta, C. Hernandez-Garcia, L. Plaja, A. Becker, A. Jaron-Becker, M. M. Murnane, and H. C. Kapteyn, “Bright coherent ultrahigh harmonics in the keV x-ray regime from mid-infrared femtosecond lasers,” Science 336, 1287–1291 (2012).
[CrossRef]

Joly, N. Y.

K. F. Mak, J. C. Travers, N. Y. Joly, A. Abdolvand, and P. St.J. Russell, “Two techniques for temporal pulse compression in gas-filled hollow-core kagomé photonic crystal fiber,” Opt. Lett. 38, 3592–3595 (2013).
[CrossRef]

K. F. Mak, J. C. Travers, P. Hölzer, N. Y. Joly, and P. St.J. Russell, “Tunable vacuum-UV to visible ultrafast pulse source based on gas-filled Kagome-PCF,” Opt. Express 21, 10942 (2013).
[CrossRef]

M. Azhar, N. Y. Joly, J. C. Travers, and P. St.J. Russell, “Nonlinear optics in Xe-filled hollow-core PCF in high pressure and supercritical regimes,” Appl. Phys. B 112, 457–460 (2013).

P. Hölzer, W. Chang, J. C. Travers, A. Nazarkin, J. Nold, N. Y. Joly, M. F. Saleh, F. Biancalana, and P. St.J. Russell, “Femtosecond nonlinear fiber optics in the ionization regime,” Phys. Rev. Lett. 107, 203901 (2011).
[CrossRef]

M. F. Saleh, W. Chang, P. Hölzer, A. Nazarkin, J. C. Travers, N. Y. Joly, P. St.J. Russell, and F. Biancalana, “Theory of photoionization-induced blueshift of ultrashort solitons in gas-filled hollow-core photonic crystal fibers,” Phys. Rev. Lett. 107, 203902 (2011).
[CrossRef]

W. Chang, A. Nazarkin, J. C. Travers, J. Nold, P. Hölzer, N. Y. Joly, and P. St.J. Russell, “Influence of ionization on ultrafast gas-based nonlinear fiber optics,” Opt. Express 19, 21018 (2011).
[CrossRef]

N. Y. Joly, J. Nold, W. Chang, P. Hölzer, A. Nazarkin, G. K. L. Wong, F. Biancalana, and P. St.J. Russell, “Bright spatially coherent wavelength-tunable deep-uv laser source using an ar-filled photonic crystal fiber,” Phys. Rev. Lett. 106, 203901 (2011).
[CrossRef]

J. C. Travers, W. Chang, J. Nold, N. Y. Joly, and P. St.J. Russell, “Ultrafast nonlinear optics in gas-filled hollow-core photonic crystal fibers,” J. Opt. Soc. Am. B 28, A11–A26 (2011).
[CrossRef]

J. Nold, P. Hölzer, N. Y. Joly, G. K. L. Wong, A. Nazarkin, A. Podlipensky, M. Scharrer, and P. St.J. Russell, “Pressure-controlled phase matching to third harmonic in Ar-filled hollow-core photonic crystal fiber,” Opt. Lett. 35, 2922–2924 (2010).
[CrossRef]

Kalashnikov, M. P.

A. Börzsönyi, Z. Heiner, M. P. Kalashnikov, A. P. Kovács, and K. Osvay, “Dispersion measurement of inert gases and gas mixtures at 800  nm,” Appl. Opt. 47, 4856–4863 (2008).
[CrossRef]

Kalosha, V. P.

V. P. Kalosha and J. Herrmann, “Phase relations, quasicontinuous spectra and subfemtosecond pulses in high-order stimulated Raman scattering with short-pulse excitation,” Phys. Rev. Lett. 85, 1226–1229 (2000).
[CrossRef]

Kapteyn, H. C.

T. Popmintchev, M.-C. Chen, D. Popmintchev, P. Arpin, S. Brown, S. Alisauskas, G. Andriukaitis, T. Balciunas, O. D. Mucke, A. Pugzlys, A. Baltuska, B. Shim, S. E. Schrauth, A. Gaeta, C. Hernandez-Garcia, L. Plaja, A. Becker, A. Jaron-Becker, M. M. Murnane, and H. C. Kapteyn, “Bright coherent ultrahigh harmonics in the keV x-ray regime from mid-infrared femtosecond lasers,” Science 336, 1287–1291 (2012).
[CrossRef]

Karlsson, M.

N. Akhmediev and M. Karlsson, “Cherenkov radiation emitted by solitons in optical fibers,” Phys. Rev. A 51, 2602–2607 (1995).
[CrossRef]

Kinsler, P.

P. Kinsler, “Optical pulse propagation with minimal approximations,” Phys. Rev. A 81, 013819 (2010).
[CrossRef]

Knight, J. C.

F. Benabid, J. C. Knight, G. Antonopoulos, and P. St.J. Russell, “Stimulated Raman scattering in hydrogen-filled hollow-core photonic crystal fiber,” Science 298, 399–402 (2002).
[CrossRef]

T. A. Birks, J. C. Knight, and P. St.J. Russell, “Endlessly single-mode photonic crystal fiber,” Opt. Lett. 22, 961–963 (1997).
[CrossRef]

Köhler, C.

C. Köhler, L. Bergé, and S. Skupin, “Effect of nonlinear dispersion on pulse self-compression in a defocusing noble gas,” Physica D 240, 963–970 (2011).
[CrossRef]

Kolesik, M.

M. Kolesik, P. Jakobsen, and J. V. Moloney, “Quantifying the limits of unidirectional ultrashort optical pulse propagation,” Phys. Rev. A 86, 035801 (2012).
[CrossRef]

A. Couairon, E. Brambilla, T. Corti, D. Majus, O. Ramírez-Góngora, and M. Kolesik, “Practitioner’s guide to laser pulse propagation models and simulation,” Eur. Phys. J. Spec. Top. 199, 5–76 (2011).
[CrossRef]

M. Kolesik and J. Moloney, “Nonlinear optical pulse propagation simulation: from Maxwell’s to unidirectional equations,” Phys. Rev. E 70, 036604 (2004).
[CrossRef]

M. Kolesik, J. V. Moloney, and M. Mlejnek, “Unidirectional optical pulse propagation equation,” Phys. Rev. Lett. 89, 283902 (2002).
[CrossRef]

Kovács, A. P.

A. Börzsönyi, Z. Heiner, M. P. Kalashnikov, A. P. Kovács, and K. Osvay, “Dispersion measurement of inert gases and gas mixtures at 800  nm,” Appl. Opt. 47, 4856–4863 (2008).
[CrossRef]

Krausz, F.

M. Geissler, G. Tempea, A. Scrinzi, M. Schnürer, F. Krausz, and T. Brabec, “Light propagation in field-ionizing media: extreme nonlinear optics,” Phys. Rev. Lett. 83, 2930–2933 (1999).
[CrossRef]

Kristensen, P.

N. Bozinovic, Y. Yue, Y. Ren, M. Tur, P. Kristensen, H. Huang, A. E. Willner, and S. Ramachandran, “Terabit-scale orbital angular momentum mode division multiplexing in fibers,” Science 340, 1545–1548 (2013).
[CrossRef]

Laegsgaard, J.

J. Laegsgaard, “Mode profile dispersion in the generalised nonlinear Schr¨dinger equation,” Opt. Express 15, 16110–16123 (2007).
[CrossRef]

Lee, Y. C.

P. K. A. Wai, H. H. Chen, and Y. C. Lee, “Radiations by ‘solitons’ at the zero group-dispersion wavelength of single-mode optical fibers,” Phys. Rev. A 41, 426–439 (1990).
[CrossRef]

Lehmeier, H. J.

H. J. Lehmeier, W. Leupacher, and A. Penzkofer, “Nonresonant third order hyperpolarizability of rare gases and N2 determined by third harmonic generation,” Opt. Commun. 56, 67–72 (1985).
[CrossRef]

Leupacher, W.

H. J. Lehmeier, W. Leupacher, and A. Penzkofer, “Nonresonant third order hyperpolarizability of rare gases and N2 determined by third harmonic generation,” Opt. Commun. 56, 67–72 (1985).
[CrossRef]

Lingle, R.

R. Ryf, S. Randel, A. H. Gnauck, C. Bolle, A. Sierra, S. Mumtaz, M. Esmaeelpour, E. C. Burrows, R.-J. Essiambre, P. J. Winzer, D. W. Peckham, A. H. McCurdy, and R. Lingle, “Mode-division multiplexing over 96  km of few-mode fiber using coherent 6×6 MIMO Processing,” J. Lightwave Technol. 30, 521–531 (2012).
[CrossRef]

Love, J.

A. W. Snyder and J. Love, Optical Waveguide Theory (Springer, 1983).

Majus, D.

A. Couairon, E. Brambilla, T. Corti, D. Majus, O. Ramírez-Góngora, and M. Kolesik, “Practitioner’s guide to laser pulse propagation models and simulation,” Eur. Phys. J. Spec. Top. 199, 5–76 (2011).
[CrossRef]

Mak, K. F.

K. F. Mak, J. C. Travers, N. Y. Joly, A. Abdolvand, and P. St.J. Russell, “Two techniques for temporal pulse compression in gas-filled hollow-core kagomé photonic crystal fiber,” Opt. Lett. 38, 3592–3595 (2013).
[CrossRef]

K. F. Mak, J. C. Travers, P. Hölzer, N. Y. Joly, and P. St.J. Russell, “Tunable vacuum-UV to visible ultrafast pulse source based on gas-filled Kagome-PCF,” Opt. Express 21, 10942 (2013).
[CrossRef]

Mamyshev, P. V.

P. V. Mamyshev and S. V. Chernikov, “Ultrashort-pulse propagation in optical fibers,” Opt. Lett. 15, 1076–1078 (1990).
[CrossRef]

Marcatili, E. A. J.

E. A. J. Marcatili and R. A. Schmeltzer, “Hollow metallic and dielectric waveguides for long distance optical transmission and lasers (long distance optical transmission in hollow dielectric and metal circular waveguides, examining normal mode propagation),” Bell Syst. Tech. J. 43, 1783–1809 (1964).
[CrossRef]

McCurdy, A. H.

R. Ryf, S. Randel, A. H. Gnauck, C. Bolle, A. Sierra, S. Mumtaz, M. Esmaeelpour, E. C. Burrows, R.-J. Essiambre, P. J. Winzer, D. W. Peckham, A. H. McCurdy, and R. Lingle, “Mode-division multiplexing over 96  km of few-mode fiber using coherent 6×6 MIMO Processing,” J. Lightwave Technol. 30, 521–531 (2012).
[CrossRef]

Menyuk, C. R.

C. R. Menyuk, “Stability of solitons in birefringent optical fibers. I: equal propagation amplitudes,” Opt. Lett. 12, 614–616 (1987).
[CrossRef]

Mlejnek, M.

M. Kolesik, J. V. Moloney, and M. Mlejnek, “Unidirectional optical pulse propagation equation,” Phys. Rev. Lett. 89, 283902 (2002).
[CrossRef]

Moloney, J.

M. Kolesik and J. Moloney, “Nonlinear optical pulse propagation simulation: from Maxwell’s to unidirectional equations,” Phys. Rev. E 70, 036604 (2004).
[CrossRef]

Moloney, J. V.

M. Kolesik, P. Jakobsen, and J. V. Moloney, “Quantifying the limits of unidirectional ultrashort optical pulse propagation,” Phys. Rev. A 86, 035801 (2012).
[CrossRef]

M. Kolesik, J. V. Moloney, and M. Mlejnek, “Unidirectional optical pulse propagation equation,” Phys. Rev. Lett. 89, 283902 (2002).
[CrossRef]

Mucke, O. D.

T. Popmintchev, M.-C. Chen, D. Popmintchev, P. Arpin, S. Brown, S. Alisauskas, G. Andriukaitis, T. Balciunas, O. D. Mucke, A. Pugzlys, A. Baltuska, B. Shim, S. E. Schrauth, A. Gaeta, C. Hernandez-Garcia, L. Plaja, A. Becker, A. Jaron-Becker, M. M. Murnane, and H. C. Kapteyn, “Bright coherent ultrahigh harmonics in the keV x-ray regime from mid-infrared femtosecond lasers,” Science 336, 1287–1291 (2012).
[CrossRef]

Mumtaz, S.

R. Ryf, S. Randel, A. H. Gnauck, C. Bolle, A. Sierra, S. Mumtaz, M. Esmaeelpour, E. C. Burrows, R.-J. Essiambre, P. J. Winzer, D. W. Peckham, A. H. McCurdy, and R. Lingle, “Mode-division multiplexing over 96  km of few-mode fiber using coherent 6×6 MIMO Processing,” J. Lightwave Technol. 30, 521–531 (2012).
[CrossRef]

Murnane, M. M.

T. Popmintchev, M.-C. Chen, D. Popmintchev, P. Arpin, S. Brown, S. Alisauskas, G. Andriukaitis, T. Balciunas, O. D. Mucke, A. Pugzlys, A. Baltuska, B. Shim, S. E. Schrauth, A. Gaeta, C. Hernandez-Garcia, L. Plaja, A. Becker, A. Jaron-Becker, M. M. Murnane, and H. C. Kapteyn, “Bright coherent ultrahigh harmonics in the keV x-ray regime from mid-infrared femtosecond lasers,” Science 336, 1287–1291 (2012).
[CrossRef]

Mysyrowicz, A.

C. L. Arnold, B. Zhou, S. Akturk, S. Chen, A. Couairon, and A. Mysyrowicz, “Pulse compression with planar hollow waveguides: a pathway towards relativistic intensity with table-top lasers,” New J. Phys. 12, 073015 (2010).
[CrossRef]

Nazarkin, A.

P. Hölzer, W. Chang, J. C. Travers, A. Nazarkin, J. Nold, N. Y. Joly, M. F. Saleh, F. Biancalana, and P. St.J. Russell, “Femtosecond nonlinear fiber optics in the ionization regime,” Phys. Rev. Lett. 107, 203901 (2011).
[CrossRef]

M. F. Saleh, W. Chang, P. Hölzer, A. Nazarkin, J. C. Travers, N. Y. Joly, P. St.J. Russell, and F. Biancalana, “Theory of photoionization-induced blueshift of ultrashort solitons in gas-filled hollow-core photonic crystal fibers,” Phys. Rev. Lett. 107, 203902 (2011).
[CrossRef]

N. Y. Joly, J. Nold, W. Chang, P. Hölzer, A. Nazarkin, G. K. L. Wong, F. Biancalana, and P. St.J. Russell, “Bright spatially coherent wavelength-tunable deep-uv laser source using an ar-filled photonic crystal fiber,” Phys. Rev. Lett. 106, 203901 (2011).
[CrossRef]

W. Chang, A. Nazarkin, J. C. Travers, J. Nold, P. Hölzer, N. Y. Joly, and P. St.J. Russell, “Influence of ionization on ultrafast gas-based nonlinear fiber optics,” Opt. Express 19, 21018 (2011).
[CrossRef]

J. Nold, P. Hölzer, N. Y. Joly, G. K. L. Wong, A. Nazarkin, A. Podlipensky, M. Scharrer, and P. St.J. Russell, “Pressure-controlled phase matching to third harmonic in Ar-filled hollow-core photonic crystal fiber,” Opt. Lett. 35, 2922–2924 (2010).
[CrossRef]

Nold, J.

P. Hölzer, W. Chang, J. C. Travers, A. Nazarkin, J. Nold, N. Y. Joly, M. F. Saleh, F. Biancalana, and P. St.J. Russell, “Femtosecond nonlinear fiber optics in the ionization regime,” Phys. Rev. Lett. 107, 203901 (2011).
[CrossRef]

W. Chang, A. Nazarkin, J. C. Travers, J. Nold, P. Hölzer, N. Y. Joly, and P. St.J. Russell, “Influence of ionization on ultrafast gas-based nonlinear fiber optics,” Opt. Express 19, 21018 (2011).
[CrossRef]

N. Y. Joly, J. Nold, W. Chang, P. Hölzer, A. Nazarkin, G. K. L. Wong, F. Biancalana, and P. St.J. Russell, “Bright spatially coherent wavelength-tunable deep-uv laser source using an ar-filled photonic crystal fiber,” Phys. Rev. Lett. 106, 203901 (2011).
[CrossRef]

J. C. Travers, W. Chang, J. Nold, N. Y. Joly, and P. St.J. Russell, “Ultrafast nonlinear optics in gas-filled hollow-core photonic crystal fibers,” J. Opt. Soc. Am. B 28, A11–A26 (2011).
[CrossRef]

J. Nold, P. Hölzer, N. Y. Joly, G. K. L. Wong, A. Nazarkin, A. Podlipensky, M. Scharrer, and P. St.J. Russell, “Pressure-controlled phase matching to third harmonic in Ar-filled hollow-core photonic crystal fiber,” Opt. Lett. 35, 2922–2924 (2010).
[CrossRef]

Nørsett, S. P.

E. Hairer, S. P. Nørsett, and G. Wanner, Solving Ordinary Differential Equations I: Nonstiff Problems (Springer, 2010).

Osvay, K.

A. Börzsönyi, Z. Heiner, M. P. Kalashnikov, A. P. Kovács, and K. Osvay, “Dispersion measurement of inert gases and gas mixtures at 800  nm,” Appl. Opt. 47, 4856–4863 (2008).
[CrossRef]

Peckham, D. W.

R. Ryf, S. Randel, A. H. Gnauck, C. Bolle, A. Sierra, S. Mumtaz, M. Esmaeelpour, E. C. Burrows, R.-J. Essiambre, P. J. Winzer, D. W. Peckham, A. H. McCurdy, and R. Lingle, “Mode-division multiplexing over 96  km of few-mode fiber using coherent 6×6 MIMO Processing,” J. Lightwave Technol. 30, 521–531 (2012).
[CrossRef]

Penzkofer, A.

H. J. Lehmeier, W. Leupacher, and A. Penzkofer, “Nonresonant third order hyperpolarizability of rare gases and N2 determined by third harmonic generation,” Opt. Commun. 56, 67–72 (1985).
[CrossRef]

Plaja, L.

T. Popmintchev, M.-C. Chen, D. Popmintchev, P. Arpin, S. Brown, S. Alisauskas, G. Andriukaitis, T. Balciunas, O. D. Mucke, A. Pugzlys, A. Baltuska, B. Shim, S. E. Schrauth, A. Gaeta, C. Hernandez-Garcia, L. Plaja, A. Becker, A. Jaron-Becker, M. M. Murnane, and H. C. Kapteyn, “Bright coherent ultrahigh harmonics in the keV x-ray regime from mid-infrared femtosecond lasers,” Science 336, 1287–1291 (2012).
[CrossRef]

Podlipensky, A.

J. Nold, P. Hölzer, N. Y. Joly, G. K. L. Wong, A. Nazarkin, A. Podlipensky, M. Scharrer, and P. St.J. Russell, “Pressure-controlled phase matching to third harmonic in Ar-filled hollow-core photonic crystal fiber,” Opt. Lett. 35, 2922–2924 (2010).
[CrossRef]

Poletti, F.

R. T. Chapman, T. J. Butcher, P. Horak, F. Poletti, J. G. Frey, and W. S. Brocklesby, “Modal effects on pump-pulse propagation in an Ar-filled capillary,” Opt. Express 18, 13279–13284 (2010).
[CrossRef]

F. Poletti and P. Horak, “Dynamics of femtosecond supercontinuum generation in multimode fibers,” Opt. Express 17, 6134–6147 (2009).
[CrossRef]

F. Poletti and P. Horak, “Description of ultrashort pulse propagation in multimode optical fibers,” J. Opt. Soc. Am. B 25, 1645–1654 (2008).
[CrossRef]

Popmintchev, D.

T. Popmintchev, M.-C. Chen, D. Popmintchev, P. Arpin, S. Brown, S. Alisauskas, G. Andriukaitis, T. Balciunas, O. D. Mucke, A. Pugzlys, A. Baltuska, B. Shim, S. E. Schrauth, A. Gaeta, C. Hernandez-Garcia, L. Plaja, A. Becker, A. Jaron-Becker, M. M. Murnane, and H. C. Kapteyn, “Bright coherent ultrahigh harmonics in the keV x-ray regime from mid-infrared femtosecond lasers,” Science 336, 1287–1291 (2012).
[CrossRef]

Popmintchev, T.

T. Popmintchev, M.-C. Chen, D. Popmintchev, P. Arpin, S. Brown, S. Alisauskas, G. Andriukaitis, T. Balciunas, O. D. Mucke, A. Pugzlys, A. Baltuska, B. Shim, S. E. Schrauth, A. Gaeta, C. Hernandez-Garcia, L. Plaja, A. Becker, A. Jaron-Becker, M. M. Murnane, and H. C. Kapteyn, “Bright coherent ultrahigh harmonics in the keV x-ray regime from mid-infrared femtosecond lasers,” Science 336, 1287–1291 (2012).
[CrossRef]

Popov, V. S.

V. S. Popov, “Tunnel and multiphoton ionization of atoms and ions in a strong laser field (Keldysh theory),” Physics-Uspekhi 47, 855–885 (2004).
[CrossRef]

Porto, P. D.

B. Crosignani and P. D. Porto, “Soliton propagation in multimode optical fibers,” Opt. Lett. 6, 329–330 (1981).
[CrossRef]

Pugzlys, A.

T. Popmintchev, M.-C. Chen, D. Popmintchev, P. Arpin, S. Brown, S. Alisauskas, G. Andriukaitis, T. Balciunas, O. D. Mucke, A. Pugzlys, A. Baltuska, B. Shim, S. E. Schrauth, A. Gaeta, C. Hernandez-Garcia, L. Plaja, A. Becker, A. Jaron-Becker, M. M. Murnane, and H. C. Kapteyn, “Bright coherent ultrahigh harmonics in the keV x-ray regime from mid-infrared femtosecond lasers,” Science 336, 1287–1291 (2012).
[CrossRef]

Rae, S. C.

S. C. Rae and K. Burnett, “Detailed simulations of plasma-induced spectral blueshifting,” Phys. Rev. A 46, 1084–1090 (1992).
[CrossRef]

Ramachandran, S.

N. Bozinovic, Y. Yue, Y. Ren, M. Tur, P. Kristensen, H. Huang, A. E. Willner, and S. Ramachandran, “Terabit-scale orbital angular momentum mode division multiplexing in fibers,” Science 340, 1545–1548 (2013).
[CrossRef]

Ramírez-Góngora, O.

A. Couairon, E. Brambilla, T. Corti, D. Majus, O. Ramírez-Góngora, and M. Kolesik, “Practitioner’s guide to laser pulse propagation models and simulation,” Eur. Phys. J. Spec. Top. 199, 5–76 (2011).
[CrossRef]

Randel, S.

R. Ryf, S. Randel, A. H. Gnauck, C. Bolle, A. Sierra, S. Mumtaz, M. Esmaeelpour, E. C. Burrows, R.-J. Essiambre, P. J. Winzer, D. W. Peckham, A. H. McCurdy, and R. Lingle, “Mode-division multiplexing over 96  km of few-mode fiber using coherent 6×6 MIMO Processing,” J. Lightwave Technol. 30, 521–531 (2012).
[CrossRef]

Ren, Y.

N. Bozinovic, Y. Yue, Y. Ren, M. Tur, P. Kristensen, H. Huang, A. E. Willner, and S. Ramachandran, “Terabit-scale orbital angular momentum mode division multiplexing in fibers,” Science 340, 1545–1548 (2013).
[CrossRef]

Renninger, W. H.

W. H. Renninger and F. W. Wise, “Optical solitons in graded-index multimode fibres,” Nat. Commun. 4, 1719 (2013).
[CrossRef]

Ryf, R.

R. Ryf, S. Randel, A. H. Gnauck, C. Bolle, A. Sierra, S. Mumtaz, M. Esmaeelpour, E. C. Burrows, R.-J. Essiambre, P. J. Winzer, D. W. Peckham, A. H. McCurdy, and R. Lingle, “Mode-division multiplexing over 96  km of few-mode fiber using coherent 6×6 MIMO Processing,” J. Lightwave Technol. 30, 521–531 (2012).
[CrossRef]

Saleh, M. F.

M. F. Saleh, W. Chang, P. Hölzer, A. Nazarkin, J. C. Travers, N. Y. Joly, P. St.J. Russell, and F. Biancalana, “Theory of photoionization-induced blueshift of ultrashort solitons in gas-filled hollow-core photonic crystal fibers,” Phys. Rev. Lett. 107, 203902 (2011).
[CrossRef]

P. Hölzer, W. Chang, J. C. Travers, A. Nazarkin, J. Nold, N. Y. Joly, M. F. Saleh, F. Biancalana, and P. St.J. Russell, “Femtosecond nonlinear fiber optics in the ionization regime,” Phys. Rev. Lett. 107, 203901 (2011).
[CrossRef]

Scharrer, M.

J. Nold, P. Hölzer, N. Y. Joly, G. K. L. Wong, A. Nazarkin, A. Podlipensky, M. Scharrer, and P. St.J. Russell, “Pressure-controlled phase matching to third harmonic in Ar-filled hollow-core photonic crystal fiber,” Opt. Lett. 35, 2922–2924 (2010).
[CrossRef]

Schmeltzer, R. A.

E. A. J. Marcatili and R. A. Schmeltzer, “Hollow metallic and dielectric waveguides for long distance optical transmission and lasers (long distance optical transmission in hollow dielectric and metal circular waveguides, examining normal mode propagation),” Bell Syst. Tech. J. 43, 1783–1809 (1964).
[CrossRef]

Schnürer, M.

M. Geissler, G. Tempea, A. Scrinzi, M. Schnürer, F. Krausz, and T. Brabec, “Light propagation in field-ionizing media: extreme nonlinear optics,” Phys. Rev. Lett. 83, 2930–2933 (1999).
[CrossRef]

Schrauth, S. E.

T. Popmintchev, M.-C. Chen, D. Popmintchev, P. Arpin, S. Brown, S. Alisauskas, G. Andriukaitis, T. Balciunas, O. D. Mucke, A. Pugzlys, A. Baltuska, B. Shim, S. E. Schrauth, A. Gaeta, C. Hernandez-Garcia, L. Plaja, A. Becker, A. Jaron-Becker, M. M. Murnane, and H. C. Kapteyn, “Bright coherent ultrahigh harmonics in the keV x-ray regime from mid-infrared femtosecond lasers,” Science 336, 1287–1291 (2012).
[CrossRef]

Scrinzi, A.

M. Geissler, G. Tempea, A. Scrinzi, M. Schnürer, F. Krausz, and T. Brabec, “Light propagation in field-ionizing media: extreme nonlinear optics,” Phys. Rev. Lett. 83, 2930–2933 (1999).
[CrossRef]

Shelton, D. P.

D. P. Shelton, “Nonlinear-optical susceptibilities of gases measured at 1064 and 1319  nm,” Phys. Rev. A 42, 2578–2592 (1990).
[CrossRef]

Shim, B.

T. Popmintchev, M.-C. Chen, D. Popmintchev, P. Arpin, S. Brown, S. Alisauskas, G. Andriukaitis, T. Balciunas, O. D. Mucke, A. Pugzlys, A. Baltuska, B. Shim, S. E. Schrauth, A. Gaeta, C. Hernandez-Garcia, L. Plaja, A. Becker, A. Jaron-Becker, M. M. Murnane, and H. C. Kapteyn, “Bright coherent ultrahigh harmonics in the keV x-ray regime from mid-infrared femtosecond lasers,” Science 336, 1287–1291 (2012).
[CrossRef]

Sierra, A.

R. Ryf, S. Randel, A. H. Gnauck, C. Bolle, A. Sierra, S. Mumtaz, M. Esmaeelpour, E. C. Burrows, R.-J. Essiambre, P. J. Winzer, D. W. Peckham, A. H. McCurdy, and R. Lingle, “Mode-division multiplexing over 96  km of few-mode fiber using coherent 6×6 MIMO Processing,” J. Lightwave Technol. 30, 521–531 (2012).
[CrossRef]

Skryabin, D. V.

A. V. Yulin, D. V. Skryabin, and P. St.J. Russell, “Four-wave mixing of linear waves and solitons in fibers with higher-orderdispersion,” Opt. Lett. 29, 2411–2413 (2004).
[CrossRef]

Skupin, S.

C. Köhler, L. Bergé, and S. Skupin, “Effect of nonlinear dispersion on pulse self-compression in a defocusing noble gas,” Physica D 240, 963–970 (2011).
[CrossRef]

I. Babushkin, S. Skupin, and J. Herrmann, “Generation of terahertz radiation from ionizing two-color laser pulses in Ar filled metallic hollow waveguides,” Opt. Express 18, 9658–9663 (2010).
[CrossRef]

Snyder, A. W.

A. W. Snyder and J. Love, Optical Waveguide Theory (Springer, 1983).

St.J. Russell, P.

M. Azhar, N. Y. Joly, J. C. Travers, and P. St.J. Russell, “Nonlinear optics in Xe-filled hollow-core PCF in high pressure and supercritical regimes,” Appl. Phys. B 112, 457–460 (2013).

F. Tani, J. C. Travers, and P. St.J. Russell, “PHz-wide supercontinua of nondispersing subcycle pulses generated by extreme modulational instability,” Phys. Rev. Lett. 111, 033902 (2013).
[CrossRef]

K. F. Mak, J. C. Travers, N. Y. Joly, A. Abdolvand, and P. St.J. Russell, “Two techniques for temporal pulse compression in gas-filled hollow-core kagomé photonic crystal fiber,” Opt. Lett. 38, 3592–3595 (2013).
[CrossRef]

W. Chang, P. Hölzer, J. C. Travers, and P. St.J. Russell, “Combined soliton pulse compression and plasma-related frequency upconversion in gas-filled photonic crystal fiber,” Opt. Lett. 38, 2984–2987 (2013).
[CrossRef]

K. F. Mak, J. C. Travers, P. Hölzer, N. Y. Joly, and P. St.J. Russell, “Tunable vacuum-UV to visible ultrafast pulse source based on gas-filled Kagome-PCF,” Opt. Express 21, 10942 (2013).
[CrossRef]

N. Y. Joly, J. Nold, W. Chang, P. Hölzer, A. Nazarkin, G. K. L. Wong, F. Biancalana, and P. St.J. Russell, “Bright spatially coherent wavelength-tunable deep-uv laser source using an ar-filled photonic crystal fiber,” Phys. Rev. Lett. 106, 203901 (2011).
[CrossRef]

P. Hölzer, W. Chang, J. C. Travers, A. Nazarkin, J. Nold, N. Y. Joly, M. F. Saleh, F. Biancalana, and P. St.J. Russell, “Femtosecond nonlinear fiber optics in the ionization regime,” Phys. Rev. Lett. 107, 203901 (2011).
[CrossRef]

M. F. Saleh, W. Chang, P. Hölzer, A. Nazarkin, J. C. Travers, N. Y. Joly, P. St.J. Russell, and F. Biancalana, “Theory of photoionization-induced blueshift of ultrashort solitons in gas-filled hollow-core photonic crystal fibers,” Phys. Rev. Lett. 107, 203902 (2011).
[CrossRef]

J. C. Travers, W. Chang, J. Nold, N. Y. Joly, and P. St.J. Russell, “Ultrafast nonlinear optics in gas-filled hollow-core photonic crystal fibers,” J. Opt. Soc. Am. B 28, A11–A26 (2011).
[CrossRef]

W. Chang, A. Nazarkin, J. C. Travers, J. Nold, P. Hölzer, N. Y. Joly, and P. St.J. Russell, “Influence of ionization on ultrafast gas-based nonlinear fiber optics,” Opt. Express 19, 21018 (2011).
[CrossRef]

J. Nold, P. Hölzer, N. Y. Joly, G. K. L. Wong, A. Nazarkin, A. Podlipensky, M. Scharrer, and P. St.J. Russell, “Pressure-controlled phase matching to third harmonic in Ar-filled hollow-core photonic crystal fiber,” Opt. Lett. 35, 2922–2924 (2010).
[CrossRef]

A. V. Yulin, D. V. Skryabin, and P. St.J. Russell, “Four-wave mixing of linear waves and solitons in fibers with higher-orderdispersion,” Opt. Lett. 29, 2411–2413 (2004).
[CrossRef]

F. Benabid, J. C. Knight, G. Antonopoulos, and P. St.J. Russell, “Stimulated Raman scattering in hydrogen-filled hollow-core photonic crystal fiber,” Science 298, 399–402 (2002).
[CrossRef]

T. A. Birks, J. C. Knight, and P. St.J. Russell, “Endlessly single-mode photonic crystal fiber,” Opt. Lett. 22, 961–963 (1997).
[CrossRef]

Stolen, R. H.

R. H. Stolen, “Raman oscillation in glass optical waveguide,” Appl. Phys. Lett. 20, 62–64 (1972).
[CrossRef]

Tani, F.

F. Tani, J. C. Travers, and P. St.J. Russell, “PHz-wide supercontinua of nondispersing subcycle pulses generated by extreme modulational instability,” Phys. Rev. Lett. 111, 033902 (2013).
[CrossRef]

Tempea, G.

M. Geissler, G. Tempea, A. Scrinzi, M. Schnürer, F. Krausz, and T. Brabec, “Light propagation in field-ionizing media: extreme nonlinear optics,” Phys. Rev. Lett. 83, 2930–2933 (1999).
[CrossRef]

G. Tempea and T. Brabec, “Theory of self-focusing in a hollow waveguide,” Opt. Lett. 23, 762–764 (1998).
[CrossRef]

Travers, J. C.

M. Azhar, N. Y. Joly, J. C. Travers, and P. St.J. Russell, “Nonlinear optics in Xe-filled hollow-core PCF in high pressure and supercritical regimes,” Appl. Phys. B 112, 457–460 (2013).

F. Tani, J. C. Travers, and P. St.J. Russell, “PHz-wide supercontinua of nondispersing subcycle pulses generated by extreme modulational instability,” Phys. Rev. Lett. 111, 033902 (2013).
[CrossRef]

K. F. Mak, J. C. Travers, N. Y. Joly, A. Abdolvand, and P. St.J. Russell, “Two techniques for temporal pulse compression in gas-filled hollow-core kagomé photonic crystal fiber,” Opt. Lett. 38, 3592–3595 (2013).
[CrossRef]

W. Chang, P. Hölzer, J. C. Travers, and P. St.J. Russell, “Combined soliton pulse compression and plasma-related frequency upconversion in gas-filled photonic crystal fiber,” Opt. Lett. 38, 2984–2987 (2013).
[CrossRef]

K. F. Mak, J. C. Travers, P. Hölzer, N. Y. Joly, and P. St.J. Russell, “Tunable vacuum-UV to visible ultrafast pulse source based on gas-filled Kagome-PCF,” Opt. Express 21, 10942 (2013).
[CrossRef]

P. Hölzer, W. Chang, J. C. Travers, A. Nazarkin, J. Nold, N. Y. Joly, M. F. Saleh, F. Biancalana, and P. St.J. Russell, “Femtosecond nonlinear fiber optics in the ionization regime,” Phys. Rev. Lett. 107, 203901 (2011).
[CrossRef]

M. F. Saleh, W. Chang, P. Hölzer, A. Nazarkin, J. C. Travers, N. Y. Joly, P. St.J. Russell, and F. Biancalana, “Theory of photoionization-induced blueshift of ultrashort solitons in gas-filled hollow-core photonic crystal fibers,” Phys. Rev. Lett. 107, 203902 (2011).
[CrossRef]

J. C. Travers, W. Chang, J. Nold, N. Y. Joly, and P. St.J. Russell, “Ultrafast nonlinear optics in gas-filled hollow-core photonic crystal fibers,” J. Opt. Soc. Am. B 28, A11–A26 (2011).
[CrossRef]

W. Chang, A. Nazarkin, J. C. Travers, J. Nold, P. Hölzer, N. Y. Joly, and P. St.J. Russell, “Influence of ionization on ultrafast gas-based nonlinear fiber optics,” Opt. Express 19, 21018 (2011).
[CrossRef]

Tur, M.

N. Bozinovic, Y. Yue, Y. Ren, M. Tur, P. Kristensen, H. Huang, A. E. Willner, and S. Ramachandran, “Terabit-scale orbital angular momentum mode division multiplexing in fibers,” Science 340, 1545–1548 (2013).
[CrossRef]

Wadsworth, W. J.

Y. Chen, W. J. Wadsworth, and T. A. Birks, “Ultraviolet four-wave mixing in the LP02 fibre mode,” Opt. Lett. 38, 3747–3750 (2013).

Wai, P. K. A.

P. K. A. Wai, H. H. Chen, and Y. C. Lee, “Radiations by ‘solitons’ at the zero group-dispersion wavelength of single-mode optical fibers,” Phys. Rev. A 41, 426–439 (1990).
[CrossRef]

Wanner, G.

E. Hairer, S. P. Nørsett, and G. Wanner, Solving Ordinary Differential Equations I: Nonstiff Problems (Springer, 2010).

Willner, A. E.

N. Bozinovic, Y. Yue, Y. Ren, M. Tur, P. Kristensen, H. Huang, A. E. Willner, and S. Ramachandran, “Terabit-scale orbital angular momentum mode division multiplexing in fibers,” Science 340, 1545–1548 (2013).
[CrossRef]

Winzer, P. J.

R. Ryf, S. Randel, A. H. Gnauck, C. Bolle, A. Sierra, S. Mumtaz, M. Esmaeelpour, E. C. Burrows, R.-J. Essiambre, P. J. Winzer, D. W. Peckham, A. H. McCurdy, and R. Lingle, “Mode-division multiplexing over 96  km of few-mode fiber using coherent 6×6 MIMO Processing,” J. Lightwave Technol. 30, 521–531 (2012).
[CrossRef]

Wise, F. W.

W. H. Renninger and F. W. Wise, “Optical solitons in graded-index multimode fibres,” Nat. Commun. 4, 1719 (2013).
[CrossRef]

Wong, G. K. L.

N. Y. Joly, J. Nold, W. Chang, P. Hölzer, A. Nazarkin, G. K. L. Wong, F. Biancalana, and P. St.J. Russell, “Bright spatially coherent wavelength-tunable deep-uv laser source using an ar-filled photonic crystal fiber,” Phys. Rev. Lett. 106, 203901 (2011).
[CrossRef]

J. Nold, P. Hölzer, N. Y. Joly, G. K. L. Wong, A. Nazarkin, A. Podlipensky, M. Scharrer, and P. St.J. Russell, “Pressure-controlled phase matching to third harmonic in Ar-filled hollow-core photonic crystal fiber,” Opt. Lett. 35, 2922–2924 (2010).
[CrossRef]

Wood, D.

K. J. Blow and D. Wood, “Theoretical description of transient stimulated Raman scattering in optical fibers,” IEEE J. Quantum Electron. 25, 2665–2673 (1989).
[CrossRef]

Yudin, G.

G. Yudin and M. Ivanov, “Nonadiabatic tunnel ionization: looking inside a laser cycle,” Phys. Rev. A 64, 013409 (2001).

Yue, Y.

N. Bozinovic, Y. Yue, Y. Ren, M. Tur, P. Kristensen, H. Huang, A. E. Willner, and S. Ramachandran, “Terabit-scale orbital angular momentum mode division multiplexing in fibers,” Science 340, 1545–1548 (2013).
[CrossRef]

Yulin, A. V.

A. V. Yulin, D. V. Skryabin, and P. St.J. Russell, “Four-wave mixing of linear waves and solitons in fibers with higher-orderdispersion,” Opt. Lett. 29, 2411–2413 (2004).
[CrossRef]

Zhou, B.

C. L. Arnold, B. Zhou, S. Akturk, S. Chen, A. Couairon, and A. Mysyrowicz, “Pulse compression with planar hollow waveguides: a pathway towards relativistic intensity with table-top lasers,” New J. Phys. 12, 073015 (2010).
[CrossRef]

Appl. Opt.

A. Börzsönyi, Z. Heiner, M. P. Kalashnikov, A. P. Kovács, and K. Osvay, “Dispersion measurement of inert gases and gas mixtures at 800  nm,” Appl. Opt. 47, 4856–4863 (2008).
[CrossRef]

Appl. Phys. B

M. Azhar, N. Y. Joly, J. C. Travers, and P. St.J. Russell, “Nonlinear optics in Xe-filled hollow-core PCF in high pressure and supercritical regimes,” Appl. Phys. B 112, 457–460 (2013).

Appl. Phys. Lett.

R. H. Stolen, “Raman oscillation in glass optical waveguide,” Appl. Phys. Lett. 20, 62–64 (1972).
[CrossRef]

E. P. Ippen, “Stimulated Brillouin scattering in optical fibers,” Appl. Phys. Lett. 21, 539–541 (1972).
[CrossRef]

Bell Syst. Tech. J.

E. A. J. Marcatili and R. A. Schmeltzer, “Hollow metallic and dielectric waveguides for long distance optical transmission and lasers (long distance optical transmission in hollow dielectric and metal circular waveguides, examining normal mode propagation),” Bell Syst. Tech. J. 43, 1783–1809 (1964).
[CrossRef]

Eur. Phys. J. Spec. Top.

A. Couairon, E. Brambilla, T. Corti, D. Majus, O. Ramírez-Góngora, and M. Kolesik, “Practitioner’s guide to laser pulse propagation models and simulation,” Eur. Phys. J. Spec. Top. 199, 5–76 (2011).
[CrossRef]

IEEE J. Quantum Electron.

K. J. Blow and D. Wood, “Theoretical description of transient stimulated Raman scattering in optical fibers,” IEEE J. Quantum Electron. 25, 2665–2673 (1989).
[CrossRef]

J. Lightwave Technol.

R. Ryf, S. Randel, A. H. Gnauck, C. Bolle, A. Sierra, S. Mumtaz, M. Esmaeelpour, E. C. Burrows, R.-J. Essiambre, P. J. Winzer, D. W. Peckham, A. H. McCurdy, and R. Lingle, “Mode-division multiplexing over 96  km of few-mode fiber using coherent 6×6 MIMO Processing,” J. Lightwave Technol. 30, 521–531 (2012).
[CrossRef]

J. Hult, “A fourth-order Runge-Kutta in the interaction picture method for simulating supercontinuum generation in optical fibers,” J. Lightwave Technol. 25, 3770–3775 (2007).
[CrossRef]

J. Opt. Soc. Am. B

J. C. Travers, W. Chang, J. Nold, N. Y. Joly, and P. St.J. Russell, “Ultrafast nonlinear optics in gas-filled hollow-core photonic crystal fibers,” J. Opt. Soc. Am. B 28, A11–A26 (2011).
[CrossRef]

F. Poletti and P. Horak, “Description of ultrashort pulse propagation in multimode optical fibers,” J. Opt. Soc. Am. B 25, 1645–1654 (2008).
[CrossRef]

Nat. Commun.

W. H. Renninger and F. W. Wise, “Optical solitons in graded-index multimode fibres,” Nat. Commun. 4, 1719 (2013).
[CrossRef]

New J. Phys.

C. L. Arnold, B. Zhou, S. Akturk, S. Chen, A. Couairon, and A. Mysyrowicz, “Pulse compression with planar hollow waveguides: a pathway towards relativistic intensity with table-top lasers,” New J. Phys. 12, 073015 (2010).
[CrossRef]

Opt. Commun.

H. J. Lehmeier, W. Leupacher, and A. Penzkofer, “Nonresonant third order hyperpolarizability of rare gases and N2 determined by third harmonic generation,” Opt. Commun. 56, 67–72 (1985).
[CrossRef]

Opt. Express

I. Babushkin, S. Skupin, and J. Herrmann, “Generation of terahertz radiation from ionizing two-color laser pulses in Ar filled metallic hollow waveguides,” Opt. Express 18, 9658–9663 (2010).
[CrossRef]

K. F. Mak, J. C. Travers, P. Hölzer, N. Y. Joly, and P. St.J. Russell, “Tunable vacuum-UV to visible ultrafast pulse source based on gas-filled Kagome-PCF,” Opt. Express 21, 10942 (2013).
[CrossRef]

W. Chang, A. Nazarkin, J. C. Travers, J. Nold, P. Hölzer, N. Y. Joly, and P. St.J. Russell, “Influence of ionization on ultrafast gas-based nonlinear fiber optics,” Opt. Express 19, 21018 (2011).
[CrossRef]

J. Laegsgaard, “Mode profile dispersion in the generalised nonlinear Schr¨dinger equation,” Opt. Express 15, 16110–16123 (2007).
[CrossRef]

F. Poletti and P. Horak, “Dynamics of femtosecond supercontinuum generation in multimode fibers,” Opt. Express 17, 6134–6147 (2009).
[CrossRef]

S.-J. Im, A. Husakou, and J. Herrmann, “Guiding properties and dispersion control of kagome lattice hollow-core photonic crystal fibers,” Opt. Express 17, 13050–13058 (2009).
[CrossRef]

R. T. Chapman, T. J. Butcher, P. Horak, F. Poletti, J. G. Frey, and W. S. Brocklesby, “Modal effects on pump-pulse propagation in an Ar-filled capillary,” Opt. Express 18, 13279–13284 (2010).
[CrossRef]

Opt. Lett.

G. Fibich and A. L. Gaeta, “Critical power for self-focusing in bulk media and in hollow waveguides,” Opt. Lett. 25, 335–337 (2000).
[CrossRef]

A. V. Yulin, D. V. Skryabin, and P. St.J. Russell, “Four-wave mixing of linear waves and solitons in fibers with higher-orderdispersion,” Opt. Lett. 29, 2411–2413 (2004).
[CrossRef]

G. Tempea and T. Brabec, “Theory of self-focusing in a hollow waveguide,” Opt. Lett. 23, 762–764 (1998).
[CrossRef]

Y. Chen, W. J. Wadsworth, and T. A. Birks, “Ultraviolet four-wave mixing in the LP02 fibre mode,” Opt. Lett. 38, 3747–3750 (2013).

K. F. Mak, J. C. Travers, N. Y. Joly, A. Abdolvand, and P. St.J. Russell, “Two techniques for temporal pulse compression in gas-filled hollow-core kagomé photonic crystal fiber,” Opt. Lett. 38, 3592–3595 (2013).
[CrossRef]

P. V. Mamyshev and S. V. Chernikov, “Ultrashort-pulse propagation in optical fibers,” Opt. Lett. 15, 1076–1078 (1990).
[CrossRef]

T. A. Birks, J. C. Knight, and P. St.J. Russell, “Endlessly single-mode photonic crystal fiber,” Opt. Lett. 22, 961–963 (1997).
[CrossRef]

W. Chang, P. Hölzer, J. C. Travers, and P. St.J. Russell, “Combined soliton pulse compression and plasma-related frequency upconversion in gas-filled photonic crystal fiber,” Opt. Lett. 38, 2984–2987 (2013).
[CrossRef]

J. Nold, P. Hölzer, N. Y. Joly, G. K. L. Wong, A. Nazarkin, A. Podlipensky, M. Scharrer, and P. St.J. Russell, “Pressure-controlled phase matching to third harmonic in Ar-filled hollow-core photonic crystal fiber,” Opt. Lett. 35, 2922–2924 (2010).
[CrossRef]

A. Hasegawa, “Self-confinement of multimode optical pulse in a glass fiber,” Opt. Lett. 5, 416–417 (1980).
[CrossRef]

B. Crosignani and P. D. Porto, “Soliton propagation in multimode optical fibers,” Opt. Lett. 6, 329–330 (1981).
[CrossRef]

C. R. Menyuk, “Stability of solitons in birefringent optical fibers. I: equal propagation amplitudes,” Opt. Lett. 12, 614–616 (1987).
[CrossRef]

Phys. Rev. A

M. Kolesik, P. Jakobsen, and J. V. Moloney, “Quantifying the limits of unidirectional ultrashort optical pulse propagation,” Phys. Rev. A 86, 035801 (2012).
[CrossRef]

P. Kinsler, “Optical pulse propagation with minimal approximations,” Phys. Rev. A 81, 013819 (2010).
[CrossRef]

P. K. A. Wai, H. H. Chen, and Y. C. Lee, “Radiations by ‘solitons’ at the zero group-dispersion wavelength of single-mode optical fibers,” Phys. Rev. A 41, 426–439 (1990).
[CrossRef]

N. Akhmediev and M. Karlsson, “Cherenkov radiation emitted by solitons in optical fibers,” Phys. Rev. A 51, 2602–2607 (1995).
[CrossRef]

S. C. Rae and K. Burnett, “Detailed simulations of plasma-induced spectral blueshifting,” Phys. Rev. A 46, 1084–1090 (1992).
[CrossRef]

G. Yudin and M. Ivanov, “Nonadiabatic tunnel ionization: looking inside a laser cycle,” Phys. Rev. A 64, 013409 (2001).

D. P. Shelton, “Nonlinear-optical susceptibilities of gases measured at 1064 and 1319  nm,” Phys. Rev. A 42, 2578–2592 (1990).
[CrossRef]

Phys. Rev. E

M. Kolesik and J. Moloney, “Nonlinear optical pulse propagation simulation: from Maxwell’s to unidirectional equations,” Phys. Rev. E 70, 036604 (2004).
[CrossRef]

Phys. Rev. Lett.

A. V. Husakou and J. Herrmann, “Supercontinuum generation of higher-order solitons by fission in photonic crystal fibers,” Phys. Rev. Lett. 87, 203901 (2001).
[CrossRef]

M. Kolesik, J. V. Moloney, and M. Mlejnek, “Unidirectional optical pulse propagation equation,” Phys. Rev. Lett. 89, 283902 (2002).
[CrossRef]

N. Y. Joly, J. Nold, W. Chang, P. Hölzer, A. Nazarkin, G. K. L. Wong, F. Biancalana, and P. St.J. Russell, “Bright spatially coherent wavelength-tunable deep-uv laser source using an ar-filled photonic crystal fiber,” Phys. Rev. Lett. 106, 203901 (2011).
[CrossRef]

F. Tani, J. C. Travers, and P. St.J. Russell, “PHz-wide supercontinua of nondispersing subcycle pulses generated by extreme modulational instability,” Phys. Rev. Lett. 111, 033902 (2013).
[CrossRef]

V. P. Kalosha and J. Herrmann, “Phase relations, quasicontinuous spectra and subfemtosecond pulses in high-order stimulated Raman scattering with short-pulse excitation,” Phys. Rev. Lett. 85, 1226–1229 (2000).
[CrossRef]

P. Hölzer, W. Chang, J. C. Travers, A. Nazarkin, J. Nold, N. Y. Joly, M. F. Saleh, F. Biancalana, and P. St.J. Russell, “Femtosecond nonlinear fiber optics in the ionization regime,” Phys. Rev. Lett. 107, 203901 (2011).
[CrossRef]

M. F. Saleh, W. Chang, P. Hölzer, A. Nazarkin, J. C. Travers, N. Y. Joly, P. St.J. Russell, and F. Biancalana, “Theory of photoionization-induced blueshift of ultrashort solitons in gas-filled hollow-core photonic crystal fibers,” Phys. Rev. Lett. 107, 203902 (2011).
[CrossRef]

M. Geissler, G. Tempea, A. Scrinzi, M. Schnürer, F. Krausz, and T. Brabec, “Light propagation in field-ionizing media: extreme nonlinear optics,” Phys. Rev. Lett. 83, 2930–2933 (1999).
[CrossRef]

Physica D

C. Köhler, L. Bergé, and S. Skupin, “Effect of nonlinear dispersion on pulse self-compression in a defocusing noble gas,” Physica D 240, 963–970 (2011).
[CrossRef]

Physics-Uspekhi

V. S. Popov, “Tunnel and multiphoton ionization of atoms and ions in a strong laser field (Keldysh theory),” Physics-Uspekhi 47, 855–885 (2004).
[CrossRef]

Rev. Mod. Phys.

J. M. Dudley, G. Genty, and S. Coen, “Supercontinuum generation in photonic crystal fiber,” Rev. Mod. Phys. 78, 1135–1184 (2006).
[CrossRef]

Science

N. Bozinovic, Y. Yue, Y. Ren, M. Tur, P. Kristensen, H. Huang, A. E. Willner, and S. Ramachandran, “Terabit-scale orbital angular momentum mode division multiplexing in fibers,” Science 340, 1545–1548 (2013).
[CrossRef]

T. Popmintchev, M.-C. Chen, D. Popmintchev, P. Arpin, S. Brown, S. Alisauskas, G. Andriukaitis, T. Balciunas, O. D. Mucke, A. Pugzlys, A. Baltuska, B. Shim, S. E. Schrauth, A. Gaeta, C. Hernandez-Garcia, L. Plaja, A. Becker, A. Jaron-Becker, M. M. Murnane, and H. C. Kapteyn, “Bright coherent ultrahigh harmonics in the keV x-ray regime from mid-infrared femtosecond lasers,” Science 336, 1287–1291 (2012).
[CrossRef]

F. Benabid, J. C. Knight, G. Antonopoulos, and P. St.J. Russell, “Stimulated Raman scattering in hydrogen-filled hollow-core photonic crystal fiber,” Science 298, 399–402 (2002).
[CrossRef]

Other

E. Hairer, S. P. Nørsett, and G. Wanner, Solving Ordinary Differential Equations I: Nonstiff Problems (Springer, 2010).

A. W. Snyder and J. Love, Optical Waveguide Theory (Springer, 1983).

P. N. Butcher and D. Cotter, The Elements of Nonlinear Optics (Cambridge University, 1991).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (9)

Fig. 1.
Fig. 1.

Integration scheme for the waveguide mode propagation model.

Fig. 2.
Fig. 2.

Calculated group velocity dispersion curves for the fundamental HE11 mode (blue) and the first two higher modes, HE12 (green) and HE13 (red). The calculations are based on a 27 μm core diameter kagomé-PCF filled with xenon at 2 bar (solid) and 7 bar (dashed). The inset shows a scanning electron micrograph of the fiber used for the experiments in Section 6.

Fig. 3.
Fig. 3.

Tunable third-harmonic generation in the HE13 mode (linear scale). (a) Experimental spectra from [24]. (b) Simulated spectra using the multimode model. In both cases a pulse with 1.3 μJ energy and 30 fs duration at 800 nm propagates through 20.5 cm of Ar-filled kagomé-PCF with 28 μm core diameter.

Fig. 4.
Fig. 4.

Numerical simulations showing intermodal FWM in kagomé-PCF (core diameter 18 μm) filled with 25 bar of Xe. (a) Spectral evolution of the HE11 mode. (b) The temporal intensity evolution of the HE11 mode. MI indicates the breakup of the leading part of the pulse in the anomalous dispersion region. (c) Spectral evolution of the HE12 mode. The zero dispersion wavelengths are marked by dotted lines and anomalous and normal dispersion regions indicated by A and N. Also shown are the phase-matched FWM pump and Stokes wavelengths in the HE11 mode and anti-Stokes wavelength in the HE12 mode.

Fig. 5.
Fig. 5.

Simulation of the propagation of a 40 fs, 0.7 μJ pulse in a kagomé-PCF (core diameter 27 μm) filled with 2.7 bar of Xe. (a) Temporal and (b) spectral evolution. A and N indicate anomalous and normal dispersion. Three modes were included in the calculation.

Fig. 6.
Fig. 6.

(a) Experimental spectra (blue curve) and corresponding simulations (gray curve) at the output of a 17 cm long kagomé-PCF (core diameter 27 μm) filled with 2.7 bar of Xe. (b) Simulated spectrum decomposed into its individual modes. Pulses of duration 40 fs and energy 0.7 μJ were used in both the experiment and the simulations.

Fig. 7.
Fig. 7.

Pressure dependence of the phase-match wavelength for dispersive waves in the HE11, HE12, and HE13 modes (solid lines), together with the central wavelengths at which the peaks appear in the experiments (points). Also shown are the near-field mode patterns measured at the fiber endface for the HE12 and HE13 modes.

Fig. 8.
Fig. 8.

Simulations of MI dynamics in the fundamental mode. A pulse with energy 5 μJ, duration 500 fs and wavelength 800 nm propagates along a kagomé-PCF (core diameter 18 μm) filled with 10 bar of Xe. (a) Temporal and (b) spectral evolution. A and N indicate anomalous and normal dispersion. (c) Magnified image of the boxed-in region in (a), showing the fine details of the “soliton shower”.

Fig. 9.
Fig. 9.

Beam radius against propagation distance, with and without ionization, in a kagomé-PCF (core diameter 18 μm) filled with 10 bar Xe and pumped with 5 μJ, 500 fs pulses at 800 nm.

Equations (26)

Equations on this page are rendered with MathJax. Learn more.

E(r,θ,z,t)=12πE˜(r,θ,z,ω)eiωtdω.
E˜(r,θ,z,ω)=jMaj(z,ω)e^j(r,θ,ω)eiβj(ω)z,
e^j(r,θ,ω)=ej(r,θ,ω)Nj(ω),
Nj(ω)=Njk(ω)δjk=12|02π0(ej×hk*)·z^rdrdθ|,
Pj(z,t)=|aj(z,t)|2=2π|0aj(z,ω)eiωtdω|2.
za˜j(ω,z)=1402π0[eiβ(ω)z+iωte^j*(ω)·tPNL(r,θ,z,t)]rdrdθdt,
E˜j(z,ω)=aj(z,ω)eiβj(ω)z,
zE˜j(z,ω)=i(βj(ω)ωv)E˜j(z,ω)+iω4P˜jNL(z,ω),
P˜jNL(z,w)=02π0e^j*(ω)P˜NL(r,θ,z,ω)rdrdθ
εNL2=r,θ,ω|P˜NL(r,θ,z,ω)jMP˜jNL(z,ω)e^j(ω)|2|P˜NL(r,θ,z,ω)|2,
P˜jNL(z,ω)=P˜NL(z,ω)02π0|e^j(ω)|2rdrdθ.
βj(ω)=kμ0ε0·02π0n2(ej×hj*)·z^rdrdθ02π0n2|ej|2rdrdθ,
zE˜(z,ω)=i(β(ω)ωv)E˜(z,ω)+iω22c2ε0β(ω)P˜NL(z,ω).
PNL(r,θ,z,t)=PK(E)+PR(E)+PIon(E),
PK(r,θ,z,t)=ε0χ(3)(ωσ;ω1,ω2,ω3,r,θ)E˜(ω1)E˜(ω2)E˜(ω3)eiωσtdω1dω2dω3,
PK(r,θ,z,t)=ε0χ(3)[E(t)·E(t)]E(t),
P˜jK(z,ω)=12πklmMQjklmFk(z,t)Fl(z,t)Fm(z,t)eiωtdt,
Qjklm=ε002π0χ(3)(r,θ)(e^j·e^k)(e^l·e^m)rdrdθ,
Fj(z,t)=12πE˜j(z,w)eiωtdω
tne=(n0ne)W(E(r,θ,z,t)),
tPIon(r,θ,z,t)=Iptne(r,θ,z,t)E(r,θ,z,t)x^+e2metne(r,θ,z,t)E(r,θ,z,t)dtx^,
P˜jIon(z,ω)=2π0e^j*(ω)·P˜Ion(r,θ,z,ω)rdr.
enm(r,θ,ω)=enmr(r,θ)r^+enmθ(r,θ)θ^enmθ(r,θ)=μ0ε01ngashnmr=Jn1(unmra)cosnθenmr(r,θ)=μ0ε01ngashnmθ=Jn1(unmra)sinnθ,
βnm(ω)=k2ngas2(ω)unm2a2,
2βHE11(ωP)βHE11(ωS)βHE1n(ωAS)+ϕNL=0,2ωPωSωAS=0,
βHE1m(ω)βHE11(ω0)+(ωω0)×ωβHE11|ω0+ϕNL=0

Metrics